04768nam 22008053 450 991096075860332120231110232453.097814704701421470470144(MiAaPQ)EBC6852907(Au-PeEL)EBL6852907(CKB)20667664900041(RPAM)22493618(OCoLC)1292081275(EXLCZ)992066766490004120220117d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe Brunn-Minkowski Inequality and a Minkowski Problem for Nonlinear Capacity1st ed.Providence :American Mathematical Society,2022.©2022.1 online resource (128 pages)Memoirs of the American Mathematical Society ;v.275"Volume 275. January 2022."Print version: Akman, Murat The Brunn-Minkowski Inequality and a Minkowski Problem for Nonlinear Capacity Providence : American Mathematical Society,c2022 9781470450526 Includes bibliographical references.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."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"--Provided by publisher.Memoirs of the American Mathematical Society Minkowski geometryInequalities (Mathematics)Nonlinear theoriesElliptic functionsHarmonic functionsPartial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equationsmscPotential theory -- Higher-dimensional theory -- Potentials and capacities, extremal lengthmscDifference and functional equations -- Functional equations and inequalities -- Functional inequalities, including subadditivity, convexity, etc.mscConvex and discrete geometry -- General convexity -- Inequalities and extremum problemsmscPartial differential equations -- Elliptic equations and systems -- Variational methods for second-order elliptic equationsmscConvex and discrete geometry -- General convexity -- Convex sets in $n$ dimensions (including convex hypersurfaces)mscPartial differential equations -- Elliptic equations and systems -- Quasilinear elliptic equations with $p$-LaplacianmscMinkowski 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.515/.3533515.353335J6031B1539B6252A4035J2052A2035J92mscAkman Murat1802239Gong Jasun1802240Hineman Jay1802241MiAaPQMiAaPQMiAaPQBOOK9910960758603321The Brunn-Minkowski Inequality and a Minkowski Problem for Nonlinear Capacity4347814UNINA