Nonlinear and non-coercive elliptic problems with integrable data

Details Nonlinear and non-coercive elliptic problems with integrable data Nonlinear and non-coercive elliptic problems with integrable data

2008-03-12

arxiv.org/abs/0803.1781v1

Advances in Mathematical Sciences and Applications 16, 1 (2006) 275--297

Mathematics

Analysis of PDEs

Scientific paper

In this paper we study existence and uniqueness of renormalized solution to the following problem $\lambda (x,u) -div a(x,Du) +\Phi (x,u)) =f$ with $f$ in $L^1$ and with Dirichlet-Neumann boundary condition. The main difficulty in this task is that in general the operator entering in the above equation is not coercive in a Sobolev space. Moreover, the possible degenerate character of $\lambda$ with respect to $u$ renders more complex the proof of uniqueness for integrable data $f$.

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