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Article Dans Une Revue Potential Analysis Année : 2015

A class of second-order linear elliptic equations with drift: renormalized solutions, uniqueness and homogenization

Résumé

In this paper a class of $N$-dimensional second-order linear elliptic equations with a drift is studied. When the drift belongs to $L^2$ the existence of a renormalized solution is proved. There is also uniqueness in the class of the renormalized solutions modulo~$L^\infty$, but the uniqueness is violated when the drift equation is regarded in the distributions sense. Then, considering a sequence of oscillating drifts which converges weakly in $L^2$ to a limit drift in $L^q$, with $q>N$, the homogenization process makes appear an extra zero-order term involving a non-negative Radon measure which does not load the zero capacity sets. This extends the homogenization result obtained in \cite{BrGe} by relaxing the equi-integrability of the drifts in $L^2$.
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Dates et versions

hal-01241032 , version 1 (09-12-2015)

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  • HAL Id : hal-01241032 , version 1

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Marc Briane, Juan Casado-Diaz. A class of second-order linear elliptic equations with drift: renormalized solutions, uniqueness and homogenization. Potential Analysis, 2015, 43 (3). ⟨hal-01241032⟩
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