On the regularity of weak solutions to $H$-systems
Copyright policy )On the regularity of weak solutions to $H$-systems
In this paper we prove that every weak solution to the H -surface equation is locally bounded, provided the prescribed mean curvature H satisfies a suitable condition at infinity. No smoothness assumption is required on H . We consider also the Dirichlet problem for the H -surface equation on a bounded regular domain with L^{\infty} boundary data and the H -bubble problem. Under the same assumptions on H , we prove that every weak solution is globally bounded.
\(H\)-surface equation, prescribed mean curvature, Minimal surfaces in differential geometry, surfaces with prescribed mean curvature, Existence theories for free problems in two or more independent variables, regularity theory
\(H\)-surface equation, prescribed mean curvature, Minimal surfaces in differential geometry, surfaces with prescribed mean curvature, Existence theories for free problems in two or more independent variables, regularity theory
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