Title: A <i>p</i>(<i>x</i>)-Laplacian extension of the Díaz-Saa inequality and some applications
Abstract:Abstract The main result of this work is a new extension of the well-known inequality by Díaz and Saa which, in our case, involves an anisotropic operator, such as the p ( x )-Laplacian, $\Delta _{p(x...Abstract The main result of this work is a new extension of the well-known inequality by Díaz and Saa which, in our case, involves an anisotropic operator, such as the p ( x )-Laplacian, $\Delta _{p(x)}u\equiv {\rm div}( \vert \nabla u \vert ^{p(x)-2}\nabla u)$ . Our present extension of this inequality enables us to establish several new results on the uniqueness of solutions and comparison principles for some anisotropic quasilinear elliptic equations. Our proofs take advantage of certain convexity properties of the energy functional associated with the p ( x )-Laplacian.Read More
Publication Year: 2019
Publication Date: 2019-01-24
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 32
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