In this paper we establish a priori bounds for positive solution of the N-Laplace equation in a bounded smooth domain in R^N, and with a nonlinearity having at most exponential growth. The techniques used in the proofs are a generalization of the methods of Brezis-Merle to the N-Laplacian, in combination with the Trudinger-Moser inequality,the Moving Planes method and a Comparison Principle for the N-Laplacian.
A priori bounds for superlinear problems involving the N-Laplacian / S. Lorca, B. Ruf, P. Ubilla. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 246:5(2009 Mar), pp. 2039-2054.
A priori bounds for superlinear problems involving the N-Laplacian
B. RufSecondo
;
2009
Abstract
In this paper we establish a priori bounds for positive solution of the N-Laplace equation in a bounded smooth domain in R^N, and with a nonlinearity having at most exponential growth. The techniques used in the proofs are a generalization of the methods of Brezis-Merle to the N-Laplacian, in combination with the Trudinger-Moser inequality,the Moving Planes method and a Comparison Principle for the N-Laplacian.
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