Variational Formulas on Lipschitz Domains

DOI10.2307/2154847zbMath0835.35036OpenAlexW4244764093MaRDI QIDQ4846052

Alan R. Elcrat, Kenneth G. Miller

Publication date: 21 March 1996

Full work available at URL: https://doi.org/10.2307/2154847

zbMATH Keywords

capacitytorsional rigidityvariational formulas

Mathematics Subject Classification ID

Vortex flows for incompressible inviscid fluids (76B47) Variational methods for second-order elliptic equations (35J20)

Related Items

Regularity of the free boundary for two-phase problems governed by divergence form equations and applications ⋮ A trial-free-boundary method for computing Batchelor flows ⋮ Up to the boundary gradient estimates for viscosity solutions to nonlinear free boundary problems with unbounded measurable ingredients ⋮ Approximate calculation of the defect of a Lipschitz cylindrical condenser ⋮ Determination of surface and interior cracks from electrostatic measurements using Schwarz-Christoffel transformations ⋮ Monotonicity theorems for Laplace Beltrami operator on Riemannian manifolds ⋮ On an isoperimetric inequality for capacity conjectured by Pólya and Szegő ⋮ An elliptic problem of the Prandtl-Batchelor type with a singularity ⋮ On two phase free boundary problems governed by elliptic equations with distributed sources ⋮ Regularity of higher order in two-phase free boundary problems ⋮ Second-order optimality conditions for constrained domain optimization ⋮ Two-phase free boundary problems: from existence to smoothness ⋮ Differentiability of potential energies with a parameter and shape sensitivity analysis for nonlinear case: the \(p\)-Poisson problem ⋮ Domain functionals and exit times for Brownian motion ⋮ Variations of constrained domain functionals associated with boundary-value problems ⋮ On a class of elliptic free boundary problems with multiple solutions ⋮ Concavity of condenser energy under boundary variations ⋮ On semilinear equations with free boundary conditions on stratified Lie groups ⋮ Free transmission problems

Cites Work

• Unnamed Item
• Unnamed Item
• Prescribing harmonic measure on convex domains
• On the existence of a solution in a domain identification problem
• Estimates of harmonic measure
• The inhomogeneous Dirichlet problem in Lipschitz domains
• Convexity of domain functionals
• A proposal concerning laminar wakes behind bluff bodies at large Reynolds number
• A Harnack inequality approach to the regularity of free boundaries part II: Flat free boundaries are Lipschitz
• Differentiation with Respect to the Domain in Boundary Value Problems
• Variational problems with two phases and their free boundaries

This page was built for publication: Variational Formulas on Lipschitz Domains