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arXiv · 0803.1781

Nonlinear and non-coercive elliptic problems with integrable data

Mohsen Ben Cheikh Ali·Olivier Guibé
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Abstract

In this paper we study existence and uniqueness of renormalized solution to the following problem $λ(x,u) -div a(x,Du) +Φ(x,u)) =f$ 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 $λ$ with respect to $u$ renders more complex the proof of uniqueness for integrable data $f$.

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Mohsen Ben Cheikh Ali, Olivier Guibé. 2008-03-12. Nonlinear and non-coercive elliptic problems with integrable data. https://arxiv.org/abs/0803.1781

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