A Picone identity for variable exponent operators and applications
2019 ◽
Vol 9
(1)
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pp. 327-360
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Keyword(s):
Abstract In this work, we establish a new Picone identity for anisotropic quasilinear operators, such as the p(x)-Laplacian defined as div(|∇ u|p(x)−2 ∇ u). Our extension provides a new version of the Diaz-Saa inequality and new uniqueness results to some quasilinear elliptic equations with variable exponents. This new Picone identity can be also used to prove some accretivity property to a class of fast diffusion equations involving variable exponents. Using this, we prove for this class of parabolic equations a new weak comparison principle.
2013 ◽
Vol 225
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pp. 79-91
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1994 ◽
Vol 124
(1)
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pp. 189-198
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2017 ◽
Vol 40
(1)
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pp. 117-142
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2010 ◽
Vol 17
(5)
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pp. 875-889
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2014 ◽
Vol 147
(1-2)
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pp. 169-191
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1985 ◽
Vol 5
(3)
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pp. 279-288
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