LEADER 04768nam 22008053 450 001 9910960758603321 005 20231110232453.0 010 $a9781470470142 010 $a1470470144 035 $a(MiAaPQ)EBC6852907 035 $a(Au-PeEL)EBL6852907 035 $a(CKB)20667664900041 035 $a(RPAM)22493618 035 $a(OCoLC)1292081275 035 $a(EXLCZ)9920667664900041 100 $a20220117d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Brunn-Minkowski Inequality and a Minkowski Problem for Nonlinear Capacity 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$dİ2022. 215 $a1 online resource (128 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.275 300 $a"Volume 275. January 2022." 311 08$aPrint version: Akman, Murat The Brunn-Minkowski Inequality and a Minkowski Problem for Nonlinear Capacity Providence : American Mathematical Society,c2022 9781470450526 320 $aIncludes bibliographical references. 327 $aNotation 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. 330 $a"In this article we study two classical potential-theoretic problems in convex geometry. The first problem is an inequality of Brunn-Minkowski type for a nonlinear capacity, CapA, where A-capacity is associated with a nonlinear elliptic PDE whose structure is modeled on the p-Laplace equation and whose solutions in an open set are called A-harmonic"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aMinkowski geometry 606 $aInequalities (Mathematics) 606 $aNonlinear theories 606 $aElliptic functions 606 $aHarmonic functions 606 $aPartial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations$2msc 606 $aPotential theory -- Higher-dimensional theory -- Potentials and capacities, extremal length$2msc 606 $aDifference and functional equations -- Functional equations and inequalities -- Functional inequalities, including subadditivity, convexity, etc.$2msc 606 $aConvex and discrete geometry -- General convexity -- Inequalities and extremum problems$2msc 606 $aPartial differential equations -- Elliptic equations and systems -- Variational methods for second-order elliptic equations$2msc 606 $aConvex and discrete geometry -- General convexity -- Convex sets in $n$ dimensions (including convex hypersurfaces)$2msc 606 $aPartial differential equations -- Elliptic equations and systems -- Quasilinear elliptic equations with $p$-Laplacian$2msc 615 0$aMinkowski geometry. 615 0$aInequalities (Mathematics) 615 0$aNonlinear theories. 615 0$aElliptic functions. 615 0$aHarmonic functions. 615 7$aPartial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations. 615 7$aPotential theory -- Higher-dimensional theory -- Potentials and capacities, extremal length. 615 7$aDifference and functional equations -- Functional equations and inequalities -- Functional inequalities, including subadditivity, convexity, etc.. 615 7$aConvex and discrete geometry -- General convexity -- Inequalities and extremum problems. 615 7$aPartial differential equations -- Elliptic equations and systems -- Variational methods for second-order elliptic equations. 615 7$aConvex and discrete geometry -- General convexity -- Convex sets in $n$ dimensions (including convex hypersurfaces). 615 7$aPartial differential equations -- Elliptic equations and systems -- Quasilinear elliptic equations with $p$-Laplacian. 676 $a515/.3533 676 $a515.3533 686 $a35J60$a31B15$a39B62$a52A40$a35J20$a52A20$a35J92$2msc 700 $aAkman$b Murat$01802239 701 $aGong$b Jasun$01802240 701 $aHineman$b Jay$01802241 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910960758603321 996 $aThe Brunn-Minkowski Inequality and a Minkowski Problem for Nonlinear Capacity$94347814 997 $aUNINA