Some monotonicity results for general systems of nonlinear elliptic PDEs

J. Brasseur; Serena Dipierro

doi:10.1016/j.jde.2016.05.017

Some monotonicity results for general systems of nonlinear elliptic PDEs

J. Brasseur, Serena Dipierro

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Abstract

© 2016 Elsevier Inc.In this paper we show that minima and stable solutions of a general energy functional of the form. ∫ΩF(∇u,∇v,u,v,x)dx enjoy some monotonicity properties, under an assumption on the growth at infinity of the energy.Our results are quite general, and comprise some rigidity results which are known in the literature.

Original language	English
Pages (from-to)	2854-2880
Journal	Journal of Differential Equations
Volume	261
Issue number	5
DOIs	https://doi.org/10.1016/j.jde.2016.05.017
Publication status	Published - 2016

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Brasseur, J., & Dipierro, S. (2016). Some monotonicity results for general systems of nonlinear elliptic PDEs. Journal of Differential Equations, 261(5), 2854-2880. https://doi.org/10.1016/j.jde.2016.05.017

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AB - © 2016 Elsevier Inc.In this paper we show that minima and stable solutions of a general energy functional of the form. ∫ΩF(∇u,∇v,u,v,x)dx enjoy some monotonicity properties, under an assumption on the growth at infinity of the energy.Our results are quite general, and comprise some rigidity results which are known in the literature.

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DO - 10.1016/j.jde.2016.05.017

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

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10.1016/j.jde.2016.05.017