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January  2009, 11(1): 131-143. doi: 10.3934/dcdsb.2009.11.131

Nondivergence elliptic equations with unbounded coefficients

1. 

Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli, Via Cintia - 80126, Napoli, Italy

2. 

Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Università degli Studi di Napoli "Federico II", Via Cintia - 80126, Napoli, Italy

Received  December 2007 Revised  January 2008 Published  November 2008

We study the nonvariational equation

$ \sum_{i,j=1}^n a_{ij}(x)\,\frac{\partial^2 u}{\partial x_i\,\partial x_j}=f$

in domains of $r^n$. We assume that the coefficients $a_{ij}$ are in $BMO$ and the equation is elliptic, but not uniformly, and consider $f$ in $L^2(r^n)$, or even in the Zygmund class $L^2\log^\alpha L(r^n)$. We also solve Dirichlet problem.

Citation: Luigi Greco, Gioconda Moscariello, Teresa Radice. Nondivergence elliptic equations with unbounded coefficients. Discrete & Continuous Dynamical Systems - B, 2009, 11 (1) : 131-143. doi: 10.3934/dcdsb.2009.11.131
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