Maximum principle gradient estimates for the capillary problem

DOI10.1080/03605308808820536zbMath0659.35042OpenAlexW2013928839MaRDI QIDQ3808538

Nicholas J. Korevaar

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1080/03605308808820536

zbMATH Keywords

maximum principleregularityLipschitz continuitybounded domainglobal estimatessingular setcapillary problema priori gradient boundscorner subdomainslocal interior and boundary estimates

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) 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 (17)

Non-parametric mean curvature flow with prescribed contact angle in Riemannian products ⋮ Mean curvature flow in a Riemannian manifold endowed with a Killing vector field ⋮ A new proof of gradient estimates for mean curvature equations with oblique boundary conditions ⋮ Gradient estimates of mean curvature equation with Neumann boundary condition in domains of Riemannian manifold ⋮ Capillary-type boundary value problems of mean curvature flows with force and transport terms on a bounded domain ⋮ Gradient estimates of mean curvature equations with Neumann boundary value problems ⋮ A mean curvature type flow with capillary boundary in a unit ball ⋮ 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 \(M^n \times \mathbb{R} \) ⋮ The comparison of capillary surfaces heights in case of small gravity ⋮ The Conormal Derivative Problem for Equations of Variational Type in Nonsmooth Domains ⋮ 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 ⋮ Mean curvature flow of Killing graphs ⋮ Gradient estimates of mean curvature equations with semi-linear oblique boundary value problems

Cites Work

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• Existence of maximal surfaces in asymptotically flat spacetimes
• Regularity of capillary surfaces over domains with corners
• On the behavior of a capillary surface at a re-entrant corner
• The conormal derivative problem for elliptic equations of variational type
• Existence and regularity of a capillary surface with prescribed contact angle
• On capillary free surfaces in a gravitational field
• Una maggiorazione a priori relativa alle ipersuperfici minimali non parametriche
• On the existence of a capillary surface with prescribed contact angle
• Static menisci in a vertical right circular cylinder

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