We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Hölder continuity of surfaces with bounded mean curvature at corners where Plateau boundaries meet free boundaries.
- Authors
Müller, Frank
- Abstract
Let $$P={\rm \Gamma}\cap{\cal S}$$ be the point of non-tangential intersection of a closed Jordan arc $${\rm \Gamma} \subset {\mathbb R}^{3}$$ and an embedded, regular support surface $${\cal S} \subset {\mathbb R}^{3}$$. Let $${\bf x}:B \to {\mathbb R}^{3}$$ be a conformally parametrized solution of $$|{\rm \Delta}{\bf x}|\le a|\nabla {\bf x}|^{2}$$with partially free boundaries $$\{{\rm \Gamma},{\cal S}\}$$. It is proved, that $${\bf x}$$ is Hölder continuous up to $$w_{0}\in \partial B$$ with $${\bf x}(w_{0})=P$$, whenever $${\bf x}$$ meets $${\cal S}$$ orthogonally along its free trace. This provides a regularity result for stationary minimal surfaces and is applicable also to surfaces of prescribed bounded mean curvature.
- Subjects
CURVATURE; GEOMETRIC surfaces; PLATEAUS; MEAN field theory; STATISTICAL mechanics; MANY-body problem
- Publication
Calculus of Variations & Partial Differential Equations, 2005, Vol 24, Issue 3, p283
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-005-0324-y