×

Unimprovable estimates in Hölder spaces for generalized solutions of the Dirichlet problem for a class of fourth order elliptic equations. (Russian) Zbl 0597.35011

The boundary value problem \[ L(u)\equiv \Delta^ 2u+\sum_{| \alpha |,| \beta | \leq 2}(-1)^{| \alpha |} {\mathcal D}^{\alpha}(a_{\quad \alpha \beta}(x){\mathcal D}^{\beta} u)=\sum_{| \alpha | \leq 2}(-1)^{| \alpha |} {\mathcal D}^{\alpha}\quad f_{\alpha},\quad x\in \Omega, \]
\[ u|_{\partial \Omega}=0,\quad (\partial u/\partial \nu)|_{\partial \Omega}=0, \] where \(\Omega\) is a domain in \({\mathbb{R}}^ 2\) and L is an elliptic operator is studied. Under suitable suppositions for \(\partial \Omega\) the best possible Hölder estimates of the generalized solution and its first derivatives near the boundary are obtained.
Reviewer: T.Genchev

MSC:

35D10 Regularity of generalized solutions of PDE (MSC2000)
35J40 Boundary value problems for higher-order elliptic equations
PDF BibTeX XML Cite
Full Text: EuDML