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Nonlinear elliptic and parabolic equations and related functional inequalities

Organizer(s):
Name:	Affiliation:	Country:
Bernhard Ruf	Accademia di Scienze e Lettere - Istituto Lombardo	Italy
Federica Sani	University of Modena and Reggio Emilia	Italy
Futoshi Takahashi	Osaka Metropolitan University	Japan

Introduction:

This Special Session will be focused on recent advances in the analysis of qualitative properties of solutions to nonlinear elliptic and parabolic equations. Key topics include existence, non-existence, uniqueness, non-uniqueness and multiplicity of solutions, as well as asymptotic behavior, blow-up, singularity formation and bubbling phenomena. Special attention will be given to the use of critical and limiting inequalities as a fundamental tool to refine the understanding of nonlinear equations. Indeed, the analysis of these equations within the Calculus of Variations is profoundly related to the development of sharp inequalities describing subtle relations between functional spaces. We hope to encourage vital discussions between researchers from Real Analysis and PDEs, fostering collaborations and connections.

All Abstracts

List of abstracts and speakers
Name	Affiliation	Title
Luca Battaglia	Universita degli Studi Roma Tre	New solutions for the Lane-Emden problem in planar domains
Marta Calanchi	Universit\`a degli Studi di Milano	Nonlinearities and singularities
Daniele Cassani	University of Insubria & RISM	Fine bounds for best constants in subcritical Sobolev`s embeddings and applications
Manuel del Pino		Singularity formation for the Keller-Segel system in the plane
Qi Guo	Renmin University of China	Recent developments in the study of nonrelativistic limit of nonlinear Dirac equations
Masato Hashizume	Osaka University	Relationship between maximizers of maximization problems and ground state solutions of semilinear elliptic equations
Norisuke Ioku	Tohoku University	Existence of solutions to a semilinear heat equation in uniformly local weak Zygmund type spaces
Michinori Ishiwata	Osaka university	On the asymptotic behavior of noncompact orbits for dynamical systems
Gabriele Mancini	University of Bari Aldo Moro	N-Euclidean Logarithmic Moser-Trudinger-Onofri inequality and some geometrical variants
Tatsuya Miura	Kyoto Univeristy	Uniqueness and minimality in Euler`s elastica problem
Monica Musso	University of Bath	Delaunay-like compact equilibria in the liquid drop model
Daisuke Naimen	Muroran Institute of Technology	Concentration and oscillation analysis of semilinear elliptic equations with exponential growth in a disc
Michiaki Onodera	Tokyo Institute of Technology	Concentrations in Bernoulli`s free boundary problem
Tohru Ozawa	Waseda University	Proof of the Brezis-Gallouet inequality via heat semigroup
Filomena Pacella	University of Roma Sapienza	Overdetermined problems in cylinders and related questions
Jyotshana Prajapat	University of Mumbai	: Global existence of solutions of a class of system of reaction-diffusion equations on evolving domains.
Prosenjit Roy	Indian Institute of Technology, Kanpur	Critical cases of Boundary Hardy and applcation to Moser-Trudinger inequality
Takeshi Suguro	Kumamoto University	Deficit estimates for an entropic form of Gagliardo-Nirenberg inequalities related to nonlinear diffusion equations and their application
Cristina Tarsi	Universit\`a degli Studi di Milano	Bifurcation into spectral gaps for Schr\odinger equations: from local to non local case
Elide Terraneo	University of Milano	Some nonlinear heat equations with exponential non-linearity and with singular data in two dimensions
Jie Wan	Beijing Institute of Technology	Recent progress in the study of concentrated helical vortices of 3d incompressible Euler equations