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This article is cited in 14 scientific papers (total in 14 papers)
$L_p$-estimates for solutions of second-order elliptic equation Dirichlet problem
A. K. Gushchin Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
Abstract:
For solutions of the Dirichlet problem for a second-order elliptic equation, we establish an analogue of the Carleson theorem on $L_p$-estimates. Under the same conditions on the coefficients for which the unique solvability of the considered problem is known, we prove this criterion for the validity of estimate of the solution norm in the space $L_p$ with a measure. We require their Dini continuity on the boundary, but we assume only their measurability and boundedness in the domain under consideration.
Keywords:
elliptic equation, Dirichlet problem, boundary value, nontangent maximal function, Carleson measure.
Received: 10.09.2012
Citation:
A. K. Gushchin, “$L_p$-estimates for solutions of second-order elliptic equation Dirichlet problem”, TMF, 174:2 (2013), 243–255; Theoret. and Math. Phys., 174:2 (2013), 209–219
Linking options:
https://www.mathnet.ru/eng/tmf8410https://doi.org/10.4213/tmf8410 https://www.mathnet.ru/eng/tmf/v174/i2/p243
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Abstract page: | 745 | Full-text PDF : | 200 | References: | 64 | First page: | 24 |
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