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Theoretical and Mathematical Physics

, Volume 174, Issue 2, pp 209–219 | Cite as

L p -estimates for solutions of second-order elliptic equation Dirichlet problem

  • A. K. GuschinEmail author
Article

Abstract

For solutions of the Dirichlet problem for a second-order elliptic equation, we establish an analogue of the Carleson theorem on Lp-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 Lp 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 

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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRASMoscowRussia

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