RENORMALIZED SOLUTIONS OF ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS

doi:10.1016/S0252-9602(17)30046-2

Abstract

Abstract:

In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the type

where 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.

Key words: elliptic equations, renormalized solution, uniqueness, Robin boundary conditions, L¹ data

Olivier GUIBÉ, Alip OROPEZA. RENORMALIZED SOLUTIONS OF ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS[J].Acta mathematica scientia,Series B, 2017, 37(4): 889-910.

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