Harnack's inequalities for solutions to the mean curvature equation and to the capillarity problem

zbMath1121.35056MaRDI QIDQ2504905

Fei-Tsen Liang

Publication date: 1 February 2007

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/108620

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Capillarity (surface tension) for incompressible inviscid fluids (76B45) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Cites Work

• Generalized solutions for the mean curvature equation
• Harnack inequalities for nonuniformly elliptic divergence structure equations
• Existence, regularity, and boundary behaviour of generalized surfaces of prescribed mean curvature
• On the regularity of solutions to variational problems in \(BV(\Omega)\)
• On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions
• Absolute gradient bounds for nonparametric hypersurfaces of constant mean curvature and the structure of generalized solutions for the constant mean curvature equation
• Una maggiorazione a priori relativa alle ipersuperfici minimali non parametriche
• Interior gradient estimates for surfaces \(z=f(x,y)\) with prescribed mean curvature
• Gradient estimates and mean curvature
• Weakly Differentiable Functions
• The problem of dirichlet for quasilinear elliptic differential equations with many independent variables
• Local estimates for gradients of solutions of non‐uniformly elliptic and parabolic equations
• The Dirichlet Problem for Surfaces of Constant Mean Curvature
• A New Proof of the Interior Gradient Bound for the Minimal Surface Equation in n Dimensions
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