Geodesic
Existence and uniqueness results for solutions of nonlinear equations with right hand side in $L^1$
Studia Mathematica, Tome 127 (1998) no. 3, pp. 223-231

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove an existence and uniqueness theorem for the elliptic Dirichlet problem for the equation div a(x,∇u) = f in a planar domain Ω. Here $f ∈ L^1(Ω)$ and the solution belongs to the so-called grand Sobolev space $W_0^{1,2)}(Ω)$. This is the proper space when the right hand side is assumed to be only $L^1$-integrable. In particular, we obtain the exponential integrability of the solution, which in the linear case was previously proved by Brezis-Merle and Chanillo-Li.
DOI : 10.4064/sm-127-3-223-231

A. Fiorenza 1 ; C. Sbordone 1

1 
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A. Fiorenza; C. Sbordone. Existence and uniqueness results for solutions of nonlinear equations with right hand side in $L^1$. Studia Mathematica, Tome 127 (1998) no. 3, pp. 223-231. doi: 10.4064/sm-127-3-223-231

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