recent trends in nonlinear partial differential equations ii · recent trends in nonlinear partial...
TRANSCRIPT
595
Recent Trends in NonlinearPartial Differential Equations II:
Stationary Problems
Workshop in Honor of Patrizia Pucci’s 60th BirthdayNonlinear Partial Differential Equations
May 28–June 1, 2012University of Perugia, Perugia, Italy
James B. SerrinEnzo L. Mitidieri
Vicentiu D. Radulescu
American Mathematical Society
Recent Trends in NonlinearPartial Differential Equations II:
Stationary ProblemsWorkshop in Honor of Patrizia Pucci’s 60th Birthday
Nonlinear Partial Differential EquationsMay 28–June 1, 2012
University of Perugia, Perugia, Italy
James B. SerrinEnzo L. Mitidieri
Vicentiu D. Radulescu
595
Recent Trends in NonlinearPartial Differential Equations II:
Stationary ProblemsWorkshop in Honor of Patrizia Pucci’s 60th Birthday
Nonlinear Partial Differential EquationsMay 28–June 1, 2012
University of Perugia, Perugia, Italy
James B. SerrinEnzo L. Mitidieri
Vicentiu D. Radulescu
American Mathematical SocietyProvidence, Rhode Island
EDITORIAL COMMITTEE
Dennis DeTurck, managing editor
Michael Loss Kailash Misra Martin J. Strauss
2010 Mathematics Subject Classification. Primary 35-06; Secondary 34-06, 35J47, 35J60,47-06, 58-06.
Frontispiece photo taken by Dr. Francesca Colasuonno at the Workshop on NonlinearPartial Differential Equations on the occasion of the 60th birthday of Professor Patrizia
Pucci at Perugia on May 30, 2012.
Library of Congress Cataloging-in-Publication Data
Workshop on nonlinear partial differential equations (2012 : Perugia, Italy)Recent trends in nonlinear partial differential equations : a workshop on nonlinear partial differ-ential equations : in honor of Patrizia Pucci’s 60th birthday, May 28–June 1, 2012, University ofPerugia, Perugia, Italy / James B. Serrin, Enzo L. Mitidieri, Vicentiu D. Radulescu, editors.
2 volumes ; cm – (Contemporary Mathematics ; volumes 594–595)Includes bibliographical references.ISBN 978-0-8218-8736-3 (alk. paper) – ISBN 978-0-8218-9861-1 (alk. paper)1. Differential equations, Nonlinear–Congresses. 2. Differential equations, Parabolic–Congresses.
I. Pucci, Patrizia, honouree. II. Serrin, J. (James), 1926–2012, editor of compilation. III. Miti-dieri, Enzo, editor of compilation. IV. Radulescu, Vicentiu D., 1958–, editor of compilation. V.Title.
QA372.W82 2012515′.353–dc23 2013017799
Contemporary Mathematics ISSN: 0271-4132 (print); ISSN: 1098-3627 (online)
DOI: http://dx.doi.org/10.1090/conm/595
Copying and reprinting. Material in this book may be reproduced by any means for edu-cational and scientific purposes without fee or permission with the exception of reproduction byservices that collect fees for delivery of documents and provided that the customary acknowledg-ment of the source is given. This consent does not extend to other kinds of copying for generaldistribution, for advertising or promotional purposes, or for resale. Requests for permission forcommercial use of material should be addressed to the Acquisitions Department, American Math-ematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests canalso be made by e-mail to [email protected].
Excluded from these provisions is material in articles for which the author holds copyright. Insuch cases, requests for permission to use or reprint should be addressed directly to the author(s).(Copyright ownership is indicated in the notice in the lower right-hand corner of the first page ofeach article.)
c© 2013 by the American Mathematical Society. All rights reserved.The American Mathematical Society retains all rightsexcept those granted to the United States Government.
Copyright of individual articles may revert to the public domain 28 yearsafter publication. Contact the AMS for copyright status of individual articles.
Printed in the United States of America.
©∞ The paper used in this book is acid-free and falls within the guidelinesestablished to ensure permanence and durability.
Visit the AMS home page at http://www.ams.org/
10 9 8 7 6 5 4 3 2 1 18 17 16 15 14 13
Contents
Thanks vii
Preface ix
On degree theory for quasilinear elliptic equations with natural growthconditions
Stefano Almi and Marco Degiovanni 1
Radial solutions for a Gelfand type quasilinear elliptic problem with quadraticgradient terms
David Arcoya, Jose Carmona,
and Pedro J. Martınez-Aparicio 21
Remarks on some quasilinear equations with gradient terms and measure dataMarie-Francoise Bidaut-Veron, Marta Garcıa-Huidobro,
and Laurent Veron 31
The effect of a linear term in some nonlinear elliptic equations with singular dataLucio Boccardo 55
Quantitative bounds for subcritical semilinear elliptic equationsMatteo Bonforte, Gabriele Grillo, and Juan Luis Vazquezo 63
Sub and supersolutions, invariant cones and multiplicity results for p-Laplaceequations
Maria-Magdalena Boureanu, Benedetta Noris,
and Susanna Terracini 91
A Moser type inequality in Zygmund spaces without boundary conditionsDaniele Cassani, Bernhard Ruf, and Cristina Tarsi 121
Existence results for some systems of coupled fractional nonlinear Schrodingerequations
Eduardo Colorado 135
Ground states for pseudo-relativistic equations with combined power andHartree-type nonlinearities
Vittorio Coti Zelati and Margherita Nolasco 151
Local boundedness of solutions to some anisotropic elliptic systemsGiovanni Cupini, Paolo Marcellini, and Elvira Mascolo 169
v
vi CONTENTS
A symmetry result for semilinear cooperative elliptic systemsLucio Damascelli, Francesca Gladiali,
and Filomena Pacella 187
An application of Kato’s inequality to quasilinear elliptic problemsLorenzo D’Ambrosio and Enzo Mitidieri 205
Multiplicity results for constrained Neumann problemsFrancesca Faraci, Antonio Iannizzotto, and Csaba Varga 219
On the classification of entire local minimizers of the Ginzburg-Landau equationAlberto Farina 231
A Liouville result on a half spaceRoberta Filippucci 237
Singular elliptic systems of Lane-Emden typeMarius Ghergu 253
Uniform estimates for polyharmonic Green functions in domains with smallholes
Hans-Christoph Grunau and Frederic Robert 263
Variational problems on the sphereGiovanni Molica Bisci 273
Semilinear Neumann problems with indefinite and unbounded potential andcrossing nonlinearity
Nikolaos S. Papageorgiou and Vicentiu D. Radulescu 293
Infinitely many solutions for fractional Laplace equations with subcriticalnonlinearity
Raffaella Servadei 317
Thanks
I wish to express my deepest thanks to Enzo Mitidieri and Vicentiu Radulescufor their immeasurable efforts and dedication in bringing to print these volumes ofcollected papers from the talks given at the May 2012 conference held in Perugiato print. I also want to convey to the authors of these works my sincerest thanksfor dedicating their excellent research and profound scientific contributions to theseproceedings, including special thanks again to the speakers and the organizers whocontributed so much to the high level of the conference in Perugia.
Regrettably, I cannot thank James Serrin in person for all his contributionsto both the Perugia conference and the publication of these volumes, as he passedaway in August of this year before it could be published. He was an enthusiasticorganizer of the May conference and played a crucial role as editor of the collectionwhich he was very much looking forward to seeing published. Even though atthe time of the conference he was already not well, he attended all the lecturesand delivered an exceptional and unforgettable opening lecture. His presence inPerugia at the conference was for me the most appreciated gift I received for my60th birthday.
James was a great mathematician and an exceptional man. His work has in-spired generations of mathematicians and will continue to influence the future ofmathematics. His loss is inconsolable for anyone who had the good fortune to meethim as I had.
Patrizia PucciPerugia, December 2012
vii
Preface
On May 11, 2012, Professor Patrizia Pucci turned 60. In celebration of PatriziaPucci’s birthday, a conference was held at the University of Perugia during May 28and June 1, 2012. The main purpose of this scientific meeting has been to bringtogether leading experts and researchers in nonlinear partial differential equations,to promote research and to stimulate interactions among the participants. Anatmosphere of particular warmth and the high scientific level made this conferencememorable. The program testified to the wide ranging influence of Professor Puccion the field of nonlinear analysis and partial differential equations. Many of thespeakers also spoke about the generosity of Patrizia in welcoming and encouragingyoung new researchers.
In her own work, Patrizia Pucci has been a seminal influence in many importantareas: the maximum principle, qualitative analysis of solutions to many classesof nonlinear PDEs (Kirchhoff problems, polyharmonic systems), mountain passtheorem in the critical case, critical exponents, variational identities, as well asvarious degenerate or singular phenomena in mathematical physics. This samebreadth is reflected in the mathematical papers included in these two volumes.
The articles in these volumes are primarily from the conference held in Perugia.They present an original view of the state of the art of many aspects of nonlinearpartial differential equations. The articles, written by mathematicians at the centerof current developments, provide somewhat more personal views of the importantdevelopments and challenges. The present volume contains contributions on thefield of nonlinear stationary partial differential equations.
We are delighted that these two volumes appear in the prestigious Contempo-rary Mathematics Series of the American Mathematical Society. We are gratefulto Sergei Gelfand, the AMS Book Program Publisher, who gave his wholeheartedsupport to this project. We address special thanks to Christine Thivierge for herprofessional guidance throughout the publication process.
Enzo L. MitidieriVicentiu D. Radulescu
ix
Selected Published Titles in This Series
595 James B. Serrin, Enzo L. Mitidieri, and Vicentiu D. Radulescu, Recent Trends inNonlinear Partial Differential Equations II, 2013
594 James B. Serrin, Enzo. L. Mitidieri, and Vicentiu D. Radulescu, Recent Trendsin Nonlinear Partial Differential Equations I, 2013
593 Anton Dzhamay, Kenichi Maruno, and Virgil U. Pierce, Algebraic and GeometricAspects of Integrable Systems and Random Matrices, 2013
592 Roland Bacher, Jerzy Weyman, Christophe Reutenauer, and Doron Zeilberger,
Noncommutative Birational Geometry, Representations and Combinatorics, 2013
591 Mark L. Agranovsky, Matania Ben-Artzi, Greg Galloway, Lavi Karp, VladimirMaz’ya, Simeon Reich, David Shoikhet, Gilbert Weinstein, and LawrenceZalcman, Complex Analysis and Dynamical Systems V, 2013
590 Ursula Hamenstadt, Alan W. Reid, Rubı Rodrıguez, Steffen Rohde,and Michael Wolf, In the Tradition of Ahlfors-Bers, VI, 2013
589 Erwan Brugalle, Maria Angelica Cueto, Alicia Dickenstein, Eva-MariaFeichtner, and Ilia Itenberg, Algebraic and Combinatorial Aspects of TropicalGeometry, 2013
588 Hristo Djidjev, R. H. Bisseling, Pierre Hansen, Dorothea Wagner, SylvainPerron, and Manuel Ruiz, Graph Partitioning and Graph Clustering, 2013
587 Wai Kiu Chan, Byeong-Kweon Oh, Takuma Hayashi, and Jeffrey D. Vaaler,Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms, 2013
586 Weimin Han, Victor Nistor, Xiaofan Li, C. S. Woodward, and Lei Shao, RecentAdvances in Scientific Computing and Applications, 2013
585 Margaret Beattie, Juan Cuadra, and A. B. Rodrıguez Raposo, Hopf Algebrasand Tensor Categories, 2013
584 Bernhelm Booß–Bavnbek, Maxim Braverman, Bruno Iochum, and CarolinaNeira Jimenez, Analysis, Geometry and Quantum Field Theory, 2012
583 Tatyana Barron, Xiaojun Chen, Brian C. Hall, Xiaobo Liu, and Claudia Polini,Mathematical Aspects of Quantization, 2012
582 Volker Diekert, Martin Kreuzer, Vladimir Shpilrain, and Xiaowen Zhang,Computational and Combinatorial Group Theory and Cryptography, 2012
581 Dong Li, Irina Mitrea, Marius Mitrea, and Shijun Zheng, Recent Advances inHarmonic Analysis and Partial Differential Equations, 2012
580 Tomoki Nakanishi, Diane Maclagan, Ian Strachan, and B. Grammaticos,Tropical Geometry and Integrable Systems, 2012
579 Masaaki Homma, Raul Figueroa, Arne Winterhof, Daniel Panario, and Leo
Storme, Theory and Applications of Finite Fields, 2012
578 D. S. Lubinsky, Peter Yuditskii, Sergey P. Suetin, and D. N. Tulyakov, RecentAdvances in Orthogonal Polynomials, Special Functions, and Their Applications, 2012
577 Enrique Zuazua, Yves Capdeboscq, Josselin Garnier, Knut Sølna, HyundaeLee, and Mikyoung Lim, Multi-Scale and High-Contrast PDE, 2012
576 Luigi Salce, Brendan Goldsmith, Peter Loth, Katrin U Tent, and Katrin UTent, Groups and Model Theory, 2012
575 Ara Basmajian and Sudeb Mitra, Quasiconformal Mappings, Riemann Surfaces, andTeichmuller Spaces, 2012
574 Yuri G. Zarhin, Masaaki Homma, and Alexander Pott, Arithmetic, Geometry,Cryptography and Coding Theory, 2012
573 Jun Hu, A. Poirier, Sudeb Mitra, and Dragomir Saric, Conformal Dynamics andHyperbolic Geometry, 2012
572 Ruben A. Hidalgo, Antonio F. Costa, and Franz Winkler, ComputationalAlgebraic and Analytic Geometry, 2012
571 Jorg Wildeshaus, Claudio Pedrini, James D. Lewis, Juan Carlos Naranjo,Wayne Raskind, and Xavier Xarles, Regulators, 2012
570 Joaquın Perez and Joaquın Perez, Geometric Analysis, 2012
SELECTED PUBLISHED TITLES IN THIS SERIES
569 V. V. Goryunov, M. J. Saia, and Jawad Snoussi, Real and Complex Singularities,2012
568 Heinz H. Bauschke, Michael Patriksson, and Ann-Brith Stromberg,Optimization Theory and Related Topics, 2012
567 Michael Boshernitzan, Rostislav Grigorchuk, and Anders Karlsson, DynamicalSystems and Group Actions, 2012
566 Andras Nemethi, Yuri Tschinkel, Alejandro Melle-Hernandez, Willem Veys,and Wilson A. Zuniga-Galindo, Zeta Functions in Algebra and Geometry, 2012
565 Toshiaki Shoji, Andrei Zelevinsky, Yoshihisa Saito, Ken-ichi Shinoda, ToshiakiShoji, and Toshiyuji Tanisaki, Algebraic Groups and Quantum Groups, 2012
564 Najmuddin Fakhruddin, Yuri Tschinkel, Elham Izadi, Janos Kollar,and Eduard Looijenga, Compact Moduli Spaces and Vector Bundles, 2012
563 Valentin Ovsienko, Federico Finkel, J. Mateos Guilarte, and M. J. Senosiain,Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and
Supersymmetric Quantum Mechanics, 2012
562 Gene Abrams, Sei-Qwon Oh, Tom Lenagan, E. S. Letzter, J. T. Stafford,and J. J. Zhang, New Trends in Noncommutative Algebra, 2012
561 Luis Rodrıguez-Piazza, Domingo Garcıa, E. A. Sanchez-Perez, and DraganVukotic, Topics in Complex Analysis and Operator Theory, 2012
560 Tsuyoshi Kobayashi, Yoav Rieck, Max Forester, Feng Luo, Robert Myers,and J. Hyam Rubinstein, Topology and Geometry in Dimension Three, 2011
559 Alexander L. Bukhgeim, Plamen Stefanov, Alexandru Tamasan, Erik L.Ritman, Plamen D Stefanov, and Gunther Uhlmann, Tomography and InverseTransport Theory, 2011
558 Gregory Cherlin, Menachem Kojman, and Karen Yeats, Model TheoreticMethods in Finite Combinatorics, 2011
557 Jeffrey Adams, Vera Serganova, and Bailin Song, Representation Theory andMathematical Physics, 2011
556 Zhonggang Zeng, Erich L. Kaltofen, Frank Sottile, and Natacha Portier,Randomization, Relaxation, and Complexity in Polynomial Equation Solving, 2011
555 Winfried Bruns, Israel Vainsencher, and Yi Zhang, Commutative Algebra and ItsConnections to Geometry, 2011
554 Mikhail Zaidenberg, Nikolai Tarkhanov, Iva Stavrov Allen, Lavi Karp, SimeonReich, David Shoikhet, Gilbert Weinstein, and Lawrence A Zalcman, ComplexAnalysis and Dynamical Systems IV: Part 2. General Relativity, Geometry, and PDE, 2011
553 Roman J. Dwilewicz, Nikolai Tarkhanov, David Shoikhet, Lavi Karp, SimeonReich, Gilbert Weinstein, and Lawrence A. Zalcman, Complex Analysis andDynamical Systems IV: Part 1. Function Theory and Optimization, 2011
552 Gunter Stolz, Daniel Ueltschi, and Michael Loss, Entropy and the Quantum II,2011
551 William Cherry, A. Khrennikov, and Alain Escassut, Advances inNon-Archimedean Analysis, 2011
550 J. Hounie, Francine Meylan, Gerson Petronilho, R. Maziani, and N. Mir,Geometric Analysis of Several Complex Variables and Related Topics, 2011
549 N. H. Ibragimov, J.-A. Weil, and J. Rodriguez Lombardero, Symmetries andRelated Topics in Differential and Difference Equations, 2011
548 Gang Bao, Chang-Ock Lee, Faouzi Triki, and Knut Sølna, Mathematical andStatistical Methods for Imaging, 2011
For a complete list of titles in this series, visit theAMS Bookstore at www.ams.org/bookstore/conmseries/.
This book is the second of two volumes that contain the proceedings of the Workshop onNonlinear Partial Differential Equations, held from May 28–June 1, 2012, at the Universityof Perugia in honor of Patrizia Pucci’s 60th birthday.
The workshop brought together leading experts and researchers in nonlinear partial dif-ferential equations to promote research and to stimulate interactions among the participants.The workshop program testified to the wide ranging influence of Patrizia Pucci on the fieldof nonlinear analysis and partial differential equations.
In her own work, Patrizia Pucci has been a seminal influence in many important areas:the maximum principle, qualitative analysis of solutions to many classes of nonlinear PDEs(Kirchhoff problems, polyharmonic systems), mountain pass theorem in the critical case,critical exponents, variational identities, as well as various degenerate or singular phenom-ena in mathematical physics. This same breadth is reflected in the mathematical papersincluded in this volume.
The companion volume (Contemporary Mathematics, Volume 594) is devoted to evolu-tion problems in nonlinear partial differential equations.
ISBN978-0-8218-9861-1
9 780821 898611
CONM/595
CO
NM
595Sta
tiona
ryPro
ble
ms
•Se
rrine
tal.,Ed
itors
AM
S