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Nonlinear Elliptic Equations in RN without Growth Restrictions on the Data

✍ Scribed by L. Boccardo; T. Gallouet; J.L. Vazquez

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
828 KB
Volume
105
Category
Article
ISSN
0022-0396

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✦ Synopsis

We show existence and regularity of solutions in (\mathbf{R}^{N}) to nonlinear elliptic equations of the form (-\operatorname{div} A(x, D u)+g(x, u)=f), when (f) is just a locally integrable function, under appropriate growth conditions on (A) and (g) but not on (f). Roughly speaking, in the model case (-A_{p}(u)+|u|^{1-1} u=f), with (p>2-(1 / N)), existence of a nonnegative solution in (\mathbf{R}^{N}) is guaranteed for every nonnegative (f \in L_{\mathrm{loc}}^{1}\left(\mathbf{R}^{N}\right)) if and only if (s>p-1). 1993 Academic Press, Inc.

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