Elliptic equations in the plane satisfying a Carleson measure condition
Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, p. 1013-1034 / Harvested from Project Euclid
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In this paper we settle (in dimension $n=2$) the open question whether for a divergence form equation $\div (A\nabla u) = 0$ with coefficients satisfying certain minimal smoothness assumption (a Carleson measure condition), the $L^p$ Neumann and Dirichlet regularity problems are solvable for some values of $p\in (1,\infty)$. The related question for the $L^p$ Dirichlet problem was settled (in any dimension) in 2001 by Kenig and Pipher [Kenig, C.E. and Pipher, J.: The Dirichlet problem for elliptic equations with drift terms. Publ. Mat. 45 (2001), no. 1, 199-217].
Publié le : 2010-09-15
Classification:  elliptic equations,  Carleson measure condition,  Neumann problem,  regularity problem,  distributional inequalities,  inhomogeneous equation,  35J25,  35J67 
@article{1282913830,
     author = {Dindo\v s
, 
Martin and Rule
, 
David J.},
     title = {Elliptic equations in the plane satisfying a Carleson measure condition},
     journal = {Rev. Mat. Iberoamericana},
     volume = {26},
     number = {1},
     year = {2010},
     pages = { 1013-1034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1282913830}
}

Dindoš
, 
Martin; Rule
, 
David J. Elliptic equations in the plane satisfying a Carleson measure condition. Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, pp.  1013-1034. http://gdmltest.u-ga.fr/item/1282913830/