# Existence and uniqueness results for solutions of nonlinear equations with right hand side in ${L}^{1}$

Studia Mathematica (1998)

- Volume: 127, Issue: 3, page 223-231
- ISSN: 0039-3223

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topFiorenza, A., and Sbordone, C.. "Existence and uniqueness results for solutions of nonlinear equations with right hand side in $L^1$." Studia Mathematica 127.3 (1998): 223-231. <http://eudml.org/doc/216469>.

@article{Fiorenza1998,

abstract = {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.},

author = {Fiorenza, A., Sbordone, C.},

journal = {Studia Mathematica},

keywords = {grand Sobolev space; exponential integrability},

language = {eng},

number = {3},

pages = {223-231},

title = {Existence and uniqueness results for solutions of nonlinear equations with right hand side in $L^1$},

url = {http://eudml.org/doc/216469},

volume = {127},

year = {1998},

}

TY - JOUR

AU - Fiorenza, A.

AU - Sbordone, C.

TI - Existence and uniqueness results for solutions of nonlinear equations with right hand side in $L^1$

JO - Studia Mathematica

PY - 1998

VL - 127

IS - 3

SP - 223

EP - 231

AB - 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.

LA - eng

KW - grand Sobolev space; exponential integrability

UR - http://eudml.org/doc/216469

ER -

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