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Endpoint solvability results for divergence form, complex elliptic equations

Mardi, 25 Septembre, 2012 - 17:00
Prénom de l'orateur : 
Mihalis
Nom de l'orateur : 
MOURGOGLOU
Résumé : 

We consider divergence form elliptic equations $Lu:=\nabla\cdot(A\nabla u)=0$ in the half space $\mathbb{R}^{n+1}_+ :=\{(x,t)\in
\mathbb{R}^n\times(0,\infty)\}$, whose coefficient matrix $A$ is complex elliptic, bounded and measurable. In addition, we suppose that $A$ satisfies some additional regularity in the direction transverse to the boundary, namely that the discrepancy $A(x,t) -A(x,0)$ 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 $L$, with data in $\la(\rn)$ (which is defined to be $BMO(\rn)$ when $\alpha=0$ and the space of H\older continuous functions $C^\alpha(\rn)$ when $\alpha \in (0

Institution de l'orateur : 
Univ. Paris 11
Thème de recherche : 
Analyse
Salle : 
04
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