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

Nondivergence elliptic equations with unbounded coefficients / Greco, Luigi; Moscariello, Gioconda; Radice, Teresa. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - STAMPA. - 11:1(2009), pp. 131-143.

Nondivergence elliptic equations with unbounded coefficients

GRECO, LUIGI;MOSCARIELLO, GIOCONDA;RADICE, TERESA
2009

Abstract

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 $\reale^n$. We assume that the coefficients $a_{ij}$ are in $BMO$ and the equation is elliptic, but not uniformly, and consider $f$ in $L^2(\reale^n)$, or even in the Zygmund class $L^2\log^\alpha L(\reale^n)$. We also solve Dirichlet problem.
2009
Nondivergence elliptic equations with unbounded coefficients / Greco, Luigi; Moscariello, Gioconda; Radice, Teresa. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - STAMPA. - 11:1(2009), pp. 131-143.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/335810
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