Réarrangement relatif dans les équations elliptiques quasi-linéaires avec un second membre distribution: Application à un théorème d'existence et de régularité
In this paper we are concerned with quasilinear elliptic equations, that is ( P ) Au + F( u,▽ u) = T in Ω ⊂ R , u ϵ W 0 1, p(Ω) ∩ L ∞(Ω) ; where A is an operator of Leray-Lions type which is defined on W 0 1 p(Ω) ∩ L ∞(Ω) (1 <p < +∞) , F is a non-linear map having a suitable growth, and T is a...
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| Published in | Journal of Differential Equations Vol. 66; no. 3; pp. 391 - 419 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | French |
| Published |
Elsevier Inc
15.03.1987
|
| Online Access | Get full text |
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| Summary: | In this paper we are concerned with quasilinear elliptic equations, that is (
P
)
Au +
F(
u,▽
u) =
T in Ω ⊂
R
, u ϵ W
0
1,
p(Ω) ∩ L
∞(Ω)
; where
A is an operator of Leray-Lions type which is defined on
W
0
1
p(Ω) ∩ L
∞(Ω) (1 <p < +∞)
,
F is a non-linear map having a suitable growth, and
T is a distribution of
W
−1,r(Ω), r >
N
(p − 1)
and r
+
̆
p
(p − 1)
. Using the techniques of the relative rearrangement (
Ann. Scuola Norm. Sup. Pisa Cl Sci (
4), in press), we give a precise a priori estimate of the solution
u of (
P
) in
L
∞-norm. These estimates allow us to prove an existence theorem for (
P
) and to get the Hölder continuity of the solution
u |
|---|---|
| ISSN: | 0022-0396 1090-2732 |
| DOI: | 10.1016/0022-0396(87)90026-X |