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Boundary regularity via Uhlenbeck–Rivière decomposition
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Frank Müller
Published/Copyright:
September 25, 2009
Abstract
We prove that weak solutions of systems with skew-symmetric structure, which possess a continuous boundary trace, have to be continuous up to the boundary. This applies, e.g., to the H-surface system Δu = 2H(u)∂x1u∧∂x2u with bounded H and thus extends an earlier result by P. Strzelecki and proves the natural counterpart of a conjecture by E. Heinz. Methodically, we use estimates below natural exponents of integrability and a recent decomposition result by T. Rivière.
Keywords: boundary regularity; systems with skew-symmetric structure; H-surface system; nonlinear decomposition
Published Online: 2009-09-25
Published in Print: 2009-07
© by Oldenbourg Wissenschaftsverlag, Duisburg, Germany
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- Preface
- Floating criteria in three dimensions
- An energy estimate for the difference of solutions for the n-dimensional equation with prescribed mean curvature and removable singularities
- Plateau’s problem for infinite contours
- Local isometric embedding of two-dimensional Riemannian metrics under geometric initial conditions
- Affine harmonic maps
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Keywords for this article
boundary regularity;
systems with skew-symmetric structure;
H-surface system;
nonlinear decomposition
Articles in the same Issue
- Preface
- Floating criteria in three dimensions
- An energy estimate for the difference of solutions for the n-dimensional equation with prescribed mean curvature and removable singularities
- Plateau’s problem for infinite contours
- Local isometric embedding of two-dimensional Riemannian metrics under geometric initial conditions
- Affine harmonic maps
- Boundary regularity via Uhlenbeck–Rivière decomposition
- Variational Heuristics for Optimal Transportation Maps on Compact Manifolds
