RENORMALIZED SOLUTIONS OF ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS

被引：0

作者：

Olivier GUIB ^{[1
]}

Alip OROPEZA ^{[1
,2
]}

机构：

[1] Laboratoire de Mathématiques Raphaёl Salem, CNRS, UMR 6085, Université de Rouen,Avenue de l'Université

[2] University of the Philippines Diliman, Institute of Mathematics

来源：

Acta Mathematica Scientia | 2017年 / 04期

关键词：

elliptic equations; renormalized solution; uniqueness; Robin boundary conditions; L~1 data;

D O I：

暂无

中图分类号：

O175.25 [椭圆型方程];

学科分类号：

070104 ;

摘要：

In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the type{-div(B（x, u）▽u) = f in ?,u = 0 on Γ;,B（x, u）▽u·n→+γ（x）h（u） =g on Γ;,where f and g are the element of L;（?） and L;（Γ;）, 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.

引用

页码：889 / 910

页数：22

共 6 条

[1] Homogenization of a quasilinear elliptic problem with nonlinear Robin boundary conditions
Cabarrubias, Bituin
Donato, Patrizia
[J]. APPLICABLE ANALYSIS, 2012, 91 (06) : 1111 - 1127
[2] Quasi-linear degenerate elliptic problems with L 1 data[J] . Nonlinear Analysis . 2004 (3)
[3] Uniqueness of solutions for some nonlinear Dirichlet problems[J] . Alessio Porretta. Nonlinear Differential Equations and Applications NoDEA . 2004 (4)
[4] Existence and uniqueness for a degenerate parabolic equation with L1-data
Andreu, F
Mazón, JM
De León, SS
Toledo, J
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 351 (01) : 285 - 306
[5] Approximated solutions of equations with L 1 data. Application to the H -convergence of quasi-linear parabolic equations[J] . Andrea Dall’Aglio. Annali di Matematica Pura ed Applicata . 1996 (1)
[6] On some nonlinear elliptic equations involving derivatives of the nonlinearity[J] . J. Carrillo,M. Chipot. Proceedings of the Royal Society of Edinburgh: Se . 1985 (3-4)

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