Abstract.
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 Ω is allowed to have infinite Lebesgue measure.
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Received: April 13, 2001; in final form: September 29, 2001¶Published online: July 9, 2002
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Dall’Aglio, A., Giachetti, D. & Puel, JP. Nonlinear elliptic equations with natural growth in general domains. Ann. Mat. Pura Appl. IV. Ser. 181, 407–426 (2002). https://doi.org/10.1007/s102310100046
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DOI: https://doi.org/10.1007/s102310100046