A p(x)-Laplacian extension of the Díaz-Saa inequality and some applications
2019 ◽
Vol 150
(1)
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pp. 205-232
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Keyword(s):
AbstractThe 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.
2019 ◽
Vol 39
(8)
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pp. 4863-4873
2017 ◽
Vol 11
(2)
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pp. 265-281
1985 ◽
Vol 5
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pp. 279-288
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1989 ◽
Vol 14
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pp. 1291-1314
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1999 ◽
Vol 329
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pp. 293-298
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2013 ◽
Vol 225
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pp. 79-91
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2006 ◽
Vol 229
(1)
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pp. 367-388
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2010 ◽
Vol 19
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pp. 255-269
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