Some Isoperimetric Inequalities for the Level Curves of Capacity and Green’s Functions on Convex Plane Domains

DOI10.1137/0519028zbMath0647.31001OpenAlexW2009302393MaRDI QIDQ3791435

Marco Longinetti

Publication date: 1988

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0519028

zbMATH Keywords

capacityGreen's functionsisoperimetric inequalitiessupport functionsymmetrizationsconvex level curves

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (10)

Conformal modulus and its reduction via mean curvatures ⋮ On the Hessian matrix and Minkowski addition of quasiconvex functions ⋮ Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces ⋮ Isoperimetric inequalities and regularity of \(a\)-harmonic functions on surfaces ⋮ Some geometric conjectures in harmonic function theory ⋮ Isoperimetric inequalities for the length of level lines of solutions of quasilinear capacity problems in the plane ⋮ Convexity properties for solutions of some second order elliptic semilinear equations ⋮ On the convexity of geometric functionals of level for solutions of certain elliptic partial differential equations ⋮ On the variational \(p\)-capacity problem in the plane ⋮ The Brunn-Minkowski Inequality and A Minkowski Problem for Nonlinear Capacity

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