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The Wiener criterion and quasilinear uniformly elliptic equations. (English) Zbl 0635.35030
The author proves the existence of a solution for a Dirichlet problem in a domain where almost all the points of the boundary satisfy a Wiener solution.

MSC:
35J60 Nonlinear elliptic equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B65 Smoothness and regularity of solutions to PDEs
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References:
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[9] J. H. Michael and W. P. Ziemer, Interior Regularity for Solutions to Obstacle Problems, J. Non-linear Anal. (to appear). · Zbl 0603.49006
[10] Wiener, N., The Dirichlet problem, J. Math. and Phys., Vol. 3, 127-146, (1924) · JFM 51.0361.01
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[12] Zibmer, W. P., The Dirichlet problem for euler‐lagrange equations on arbitrary domains, J. London Math. Soc., Vol. 19, 2, 481-487, (1979) · Zbl 0458.35037
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