The Brunn-Minkowski Inequality and a Minkowski Problem for Nonlinear Capacity

• Record Nr.: UNINA9910960758603321
• Autore: Akman Murat
• Pubbl/distr/stampa: Providence : , : American Mathematical Society, , 2022; ©2022
• ISBN: 9781470470142; 1470470144
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (128 pages)
• Collana: Memoirs of the American Mathematical Society ; ; v.275
• Classificazione: 35J6031B1539B6252A4035J2052A2035J92
• Altri autori (Persone): GongJasun; HinemanJay
• Disciplina: 515/.3533; 515.3533
• Soggetti: Minkowski geometry; Inequalities (Mathematics); Nonlinear theories; Elliptic functions; Harmonic functions; Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations; Potential theory -- Higher-dimensional theory -- Potentials and capacities, extremal length; Difference and functional equations -- Functional equations and inequalities -- Functional inequalities, including subadditivity, convexity, etc; Convex and discrete geometry -- General convexity -- Inequalities and extremum problems; Partial differential equations -- Elliptic equations and systems -- Variational methods for second-order elliptic equations; Convex and discrete geometry -- General convexity -- Convex sets in $n$ dimensions (including convex hypersurfaces); Partial differential equations -- Elliptic equations and systems -- Quasilinear elliptic equations with $p$-Laplacian
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 275. January 2022."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Notation and statement of results -- Basic estimates for A-harmonic functions -- Preliminary reductions for the proof of theorem A -- Proof of theorem A -- Final proof of theorem A -- Appendix -- Introduction and statement of results -- Boundary behavior of A-harmonic functions in Lipschitz domains -- Boundary Harnack inequalities -- Weak convergence of certain measures on Sn-1 -- The Hadamard variational formula for nonlinear capacity -- Proof of theorem B.
• Sommario/riassunto: "In this article we study two classical potential-theoretic problems in convex geometry. The first problem is an inequality of Brunn-Minkowski type for a nonlinear capacity, CapA, where A-capacity is associated with a nonlinear elliptic PDE whose structure is modeled on the p-Laplace equation and whose solutions in an open set are called A-harmonic"--