C(1,1/3)-regularity in the Dirichlet problem for Δ∞
| Autor: | Rahul Jain, B. R. Nagaraj |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Dirichlet problem
Pure mathematics 010102 general mathematics Mathematical analysis Open set Boundary (topology) 16. Peace & justice Lebesgue integration Lipschitz continuity 01 natural sciences 010101 applied mathematics Computational Mathematics symbols.namesake Computational Theory and Mathematics Modeling and Simulation Infinity Laplacian symbols Partial derivative 0101 mathematics Viscosity solution Mathematics |
| Zdroj: | Computers & Mathematics with Applications. 53:377-394 |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/j.camwa.2006.02.047 |
| Popis: | We answer the much sought after question on regularity of the viscosity solution u to the Dirichlet problem for the infinity Laplacian @D"~ in x=(x"1,...,x"n)@?R^n (n>=1) with Lipschitz boundary data on @?U of the open set U (whether u is C^1(U)), that in fact u has Holder regularity C^(^1^,^1^/^3^)(U). Furthermore, if each of the first partials u"x"""j never vanishes in [email protected]? (a coordinate dependent condition) then [email protected]?C^(^1^,^1^)(U). The methods that we employ are distinctly different from what is generally practiced in the viscosity methods of solution, and include 'action' of boundary distributions, Lebesgue differentiation and regularization near the boundary and a definition of product of distributions not satisfying the Hormander condition on their wavefront sets, while representing the first partial derivatives of u purely in terms of boundary integrals involving only first order derivatives of u on the boundary. |
| Databáze: | OpenAIRE |
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