# The Wiener test for higher order elliptic equations

@article{Mazya2002TheWT, title={The Wiener test for higher order elliptic equations}, author={Vladimir Maz'ya}, journal={arXiv: Analysis of PDEs}, year={2002} }

Wiener's criterion for the regularity of a boundary point with respect to the Dirichlet problem for the Laplace equation has been extended to various classes of elliptic and parabolic partial differential equations. They include linear divergence and nondivergence equations with discontinuous coefficients, equations with degenerate quadratic form, quasilinear and fully nonlinear equations, as well as equations on Riemannian manifolds, graphs, groups, and metric spaces. A common feature of these… Expand

#### 16 Citations

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The classical problem of regularity of boundary characteristic points for semilinear heat equations with homogeneous Dirichlet conditions is considered. The Petrovskii $ \left( {2\sqrt {{\log \log }}… Expand

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The behavior of solutions to the biharmonic equation is well-understood in smooth domains. In the past two decades substantial progress has also been made for the polyhedral domains and domains with… Expand

Polyharmonic capacity and Wiener test of higher order

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In the present paper we establish the Wiener test for boundary regularity of the solutions to the polyharmonic operator. We introduce a new notion of polyharmonic capacity and demonstrate necessary… Expand

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On estimates of biharmonic functions on Lipschitz and convex domains

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A collection of sharp dilation invariant inequalities for differentiable functions

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Abstract. We find best constants in several dilation invariant integral inequalities involving derivatives of functions. Some of these inequalities are new and some were known without best constants.… Expand

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