## $L^p$ and endpoint solvability results for divergence form elliptic equations with complex $L^\infty$ coefficients

### Lundi 28 janvier 2013 14:00-15:00 - Mihalis Mourgoglou - Université Paris-Sud

Résumé : We consider divergence form elliptic equations in the half space , whose coefficient matrix is complex elliptic, bounded and measurable. In addition, we suppose that satisfies some additional regularity in the direction transverse to the boundary, namely that the discrepancy satisfies a Carleson measure condition of Fefferman-Kenig-Pipher type, with small Carleson norm. Under these conditions, we obtain solvability of the Dirichlet problem for , with data in , , or in (which is defined to be when and when ), for , where is the De Giorgi-Nash exponent, and solvability of the Neumann and Regularity problems, with data in the spaces and respectively, for , assuming that we have bounded Layer Potentials in , and invertible Layer Potentials in and for the -independent operator .

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$L^p$ and endpoint solvability results for divergence form elliptic equations with complex $L^\infty$ coefficients  Version PDF
janvier 2019 :
 Département de Mathématiques Bâtiment 307 Faculté des Sciences d'Orsay Université Paris-Sud F-91405 Orsay Cedex Tél. : +33 (0) 1-69-15-79-56 Département Laboratoire Formation