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Continuity at boundary points of solutions of quasilinear elliptic equations with a nonstandard growth condition. (English. Russian original) Zbl 1167.35385
Izv. Math. 68, No. 6, 1063-1117 (2004); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 68, No. 6, 3-60 (2004).
The authors consider the equation $Lu:= \text{div}(|\nabla u|^{p(x)- 2}\nabla u)= 0,\tag{1}$ where $$p(x)$$ is a function measurable in $$\Omega$$ such that $1< p_1\leq p(x)\leq p_2< \infty.$ The authors investigate the behaviour at boundary points of a solution of the Dirichlet problem associated to (1), where $$\Omega$$ is a bounded domain and $$p(x)$$ satisfies some natural additional assumptions. Moreover, they obtain a regularity criterion for a boundary point of Wiener type, an estimate for the modulus of continuity of the solution near a regular boundary joint, and geometric conditions for regularity.

##### MSC:
 35J67 Boundary values of solutions to elliptic equations and elliptic systems 35J60 Nonlinear elliptic equations
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