Existence and uniqueness results for solutions of nonlinear equations with right hand side in
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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