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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 174, Number 2, Pages 243–255
DOI: https://doi.org/10.4213/tmf8410
(Mi tmf8410)
 

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
References:
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
English version:
Theoretical and Mathematical Physics, 2013, Volume 174, Issue 2, Pages 209–219
DOI: https://doi.org/10.1007/s11232-013-0018-0
Bibliographic databases:
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf8410
  • https://doi.org/10.4213/tmf8410
  • https://www.mathnet.ru/eng/tmf/v174/i2/p243
  • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:64
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