Calculus of Variations and Geometric Measure Theory
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A. Dall'Aglio - D. Giachetti - J. P. Puel

Nonlinear elliptic equations with natural growth in general domains

created on 05 Oct 2004


Published Paper

Inserted: 5 oct 2004

Journal: Annali di Matematica Pura e Applicata
Volume: 181
Pages: 407-426
Year: 2002


We prove the existence of solutions of nonlinear elliptic equations with first order terms having ``natural growth'' with respect to the gradient. The assumptions on the source terms lead to the existence of possibly unbounded solutions (though with exponential integrability). The domain $\Om$ is allowed to have infinite Lebesgue measure.

Keywords: Nonlinear elliptic equations, Gradient terms with natural growth, Unbounded solutions, A priori estimates

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