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This article is cited in 65 scientific papers (total in 65 papers)
Continuity at boundary points of solutions of quasilinear elliptic equations with a non-standard growth condition
Yu. A. Alkhutov, O. V. Krasheninnikova
Abstract:
We study the behaviour at boundary points of a solution of the Dirichlet problem with continuous boundary function for the Euler equation generated by the Lagrangian $|\nabla u|^{p(x)}/p(x)$ with variable$p=p(x)$ that has logarithmic modulus of continuity and satisfies the condition $1<p_1\leqslant p(x)\leqslant p_2<\infty$. We 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 point, and geometric conditions for regularity.
Received: 25.02.2004
Citation:
Yu. A. Alkhutov, O. V. Krasheninnikova, “Continuity at boundary points of solutions of quasilinear elliptic equations with a non-standard growth condition”, Izv. Math., 68:6 (2004), 1063–1117
Linking options:
https://www.mathnet.ru/eng/im509https://doi.org/10.1070/IM2004v068n06ABEH000509 https://www.mathnet.ru/eng/im/v68/i6/p3
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Abstract page: | 929 | Russian version PDF: | 359 | English version PDF: | 47 | References: | 97 | First page: | 2 |
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