Prescribing harmonic measure on convex domains

DOI10.1007/BF01232271zbMath0754.31007MaRDI QIDQ1177905

David S. Jerison

Publication date: 26 June 1992

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143917

zbMATH Keywords

harmonic measureMonge-Ampère equationMinkowski problem

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Potential theory on Riemannian manifolds and other spaces (31C12)

Related Items (13)

Hadamard variational formulas for \(p\)-torsion and \(p\)-eigenvalue with applications ⋮ A Minkowski problem for electrostatic capacity ⋮ The Hadamard variational formula and the Minkowski problem for \(p\)-capacity ⋮ The functional Orlicz–Brunn–Minkowski inequality for q‐torsional rigidity ⋮ A Gauss curvature flow approach to the torsional Minkowski problem ⋮ From the Brunn-Minkowski inequality to a class of generalized Poincaré-type inequalities for torsional rigidity ⋮ FROM THE BRUNN–MINKOWSKI INEQUALITY TO A CLASS OF POINCARÉ-TYPE INEQUALITIES ⋮ A \(L_p\) Brunn-Minkowski theory for logarithmic capacity ⋮ Prescribing capacitary curvature measures on planar convex domains ⋮ Variational Formulas on Lipschitz Domains ⋮ Flux \& radii within the subconformal capacity ⋮ The \(L_p\) Minkowski problem for torsion ⋮ The L_p Minkowski problem for q-capacity

Cites Work

• Interior a priori estimates for solutions of fully nonlinear equations
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• Differentiation of integrals in \(\mathbb{R}^n\)
• Estimates of harmonic measure
• Convexity of domain functionals
• Harmonic measure in convex domains
• The quasilinear dirichlet problem with decreased regularity at the boundary
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• On the regularity of the solution of then-dimensional Minkowski problem
• Isoperimetric Inequalities and Their Applications
• On the Boundary Values of Harmonic Functions
• Positive Harmonic Functions on Lipschitz Domains
• Unnamed Item
• Unnamed Item

This page was built for publication: Prescribing harmonic measure on convex domains