Renormalized solutions of elliptic equations with Robin boundary conditions |
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Authors: | Olivier GUIBÉ Alip OROPEZA |
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Affiliation: | 1. Laboratoire de Mathématiques Raphaël Salem, CNRS, UMR 6085, Université de Rouen, Avenue de l''Université, BP 12, 76801 Saint-Étienne du Rouvray cedex, France;2. University of the Philippines Diliman, Institute of Mathematics, 1101 Diliman, Quezon City, Philippines |
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Abstract: | In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the typewhere f and g are the element of L1 (Ω) and L1 (Γ1), respectively. We define a notion of renormalized solution and we prove the existence of a solution. Under additional assumptions on the matrix field B we show that the renormalized solution is unique. |
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Keywords: | elliptic equations renormalized solution uniqueness Robin boundary conditions 35J66 35A01 35A02 35R05 |
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