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Zbl 0810.35021
Boccardo, Lucio; Gallouët, Thierry; Vazquez, Juan Luis
Nonlinear elliptic equations in $\bbfR\sp N$ without growth restrictions on the data.
(English)
[J] J. Differ. Equations 105, No.2, 334-363 (1993). ISSN 0022-0396

The authors examine equations of the form (*) $-\text{div } A(x,Du)+ g(x,u) =f$, where the principal part of the operator, $-\text{div } A(x,Du)$ acts like the $p$-Laplacian. Provided $ug(x,u)$ goes to infinity fast enough as $\vert u\vert\to\infty$, they show that equation (*) has a distributional solution in $\bbfR\sp N$ for any locally integrable function $f$. In addition, the gradient of this solution, which is only assumed to be locally in $L\sp{p-1}$, is locally in $L\sp q$ for some $q>p-1$; the exponent $q$ is given explicitly in terms of $p$, $N$, and the growth of $g$.
[G.M.Lieberman (Ames)]
MSC 2000:
*35J60 Nonlinear elliptic equations
35D10 Regularity of generalized solutions of PDE

Keywords: estimates of the gradient; $p$-Laplacian

Cited in: Zbl 0863.35039

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