Gradient estimates for capillary-type problems via the maximum principle

DOI10.1080/03605308808820537zbMath0659.35043OpenAlexW2032011249MaRDI QIDQ3808539

Gary M. Lieberman

Publication date: 1988

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605308808820537

zbMATH Keywords

maximum principlebounded domainoblique derivativecapillary problemestimates for the gradient

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Maximum principles in context of PDEs (35B50) A priori estimates in context of PDEs (35B45)

Related Items (14)

A new proof of gradient estimates for mean curvature equations with oblique boundary conditions ⋮ Bounded and unbounded capillary surfaces derived from the catenoid ⋮ Gradient estimates of mean curvature equation with Neumann boundary condition in domains of Riemannian manifold ⋮ Gradient estimates of mean curvature equations with Neumann boundary value problems ⋮ Higher genus capillary surfaces in the unit ball of \(\mathbb R^3\) ⋮ ESTIMATE FOR EVOLUTIONARY SURFACES OF PRESCRIBED MEAN CURVATURE AND THE CONVERGENCE ⋮ Mean curvature type flows of graphs with nonzero Neumann boundary data in product manifold \(M^n \times \mathbb{R} \) ⋮ Mean curvature flow of graphs with Neumann boundary conditions ⋮ The comparison of capillary surfaces heights in case of small gravity ⋮ Gradient estimates for semi-linear elliptic equations with prescribed contact angle problem ⋮ Gradient estimates for elliptic oblique derivative problems via the maximum principle ⋮ Gradient estimates for capillary-type problems via the maximum principle, a second look ⋮ Translating solutions of non-parametric mean curvature flows with capillary-type boundary value problems ⋮ Gradient estimates of mean curvature equations with semi-linear oblique boundary value problems

Cites Work

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• Regularized distance and its applications
• Intermediate Schauder estimates
• The conormal derivative problem for elliptic equations of variational type
• Existence and regularity of a capillary surface with prescribed contact angle
• Una maggiorazione a priori relativa alle ipersuperfici minimali non parametriche
• The nonlinear oblique derivative problem for quasilinear elliptic equations
• The dirichlet problem for quasilinear elliptic equations with continuously differentiable boundary data
• Gradient bounds for solutions of nonuniformly elliptic oblique derivative problems
• On the existence of a capillary surface with prescribed contact angle
• Local estimates for gradients of solutions of non‐uniformly elliptic and parabolic equations

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