This book collects recent research papers by respected specialists in the field. It presents advances in the field of geometric properties for parabolic and elliptic partial differential equations, an area that has always attracted great attention. It settles the basic issues (existence, uniqueness, stability and regularity of solutions of initial/boundary value problems) before focusing on the topological and/or geometric aspects. These topics interact with many other areas of research and rely on a wide range of mathematical tools and techniques, both analytic and geometric. The Italian and Japanese mathematical schools have a long history of research on PDEs and have numerous active groups collaborating in the study of the geometric properties of their solutions.
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1 Angela Alberico, Giuseppina di Blasio and Filomena Feo: Estimates for solutions to anisotropic elliptic equations with zero order term.- 2 Vieri Benci and Lorenzo Luperi Baglini: A topological approach to non-Archimedean Mathematics.- 3 Chiara Bianchini and Giulio Ciraolo: A note on an overdetermined problem for the capacitary potential.- 4 Lorenzo Brasco and Filippo Santambrogio: Poincar´e inequalities on convex sets by Optimal Transport methods.- 5 Davide Buoso: Analyticity and criticality results for the eigenvalues of the biharmonic operator.- 6 Giulio Ciraolo and Luigi Vezzoni: A remark on an overdetermined problem in Riemannian Geometry.- 7 Norisuke Ioku and Michinori Ishiwata: A note on the scale invariant structure of critical Hardy inequalities.- 8 Yoshihito Kohsaka: Stability analysis of Delaunay surfaces as steady states for the surface diffusion equation.- 9 Rolando Magnanini and Giorgio Poggesi: Littlewood’s fourth principle.- 10 Kazuhiro Ishige and Kazushige Nakagawa: The Phragmèn-Lindelöf theorem for a fully nonlinear elliptic problem with a dynamical boundary condition.- 11 Saori Nakamori and Kazuhiro Takimoto: Entire solutions to generalized parabolic k-Hessian equations.- 12 Kurumi Hiruko and Shinya Okabe: Dynamical aspects of a hybrid system describing intermittent androgen suppression therapy of prostate cancer.- 13 Shigeru Sakaguchi: Symmetry problems on stationary isothermic surfaces in Euclidean spaces.- 14 Megumi Sano and Futoshi Takahashi: Improved Rellich type inequalities in RN.- 15 Jin Takahashi: Solvability of a Semilinear Parabolic Equation with Measures as Initial Data.- 16 Jann-Long Chern and Eiji Yanagida: Singular Solutions of the Scalar Field Equation with a Critical Exponent.
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