Global gradient estimates for nonlinear parabolic operators
2021 ◽
Vol 27
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pp. 21
Keyword(s):
We consider a parabolic equation driven by a nonlinear diffusive operator and we obtain a gradient estimate in the domain where the equation takes place. This estimate depends on the structural constants of the equation, on the geometry of the ambient space and on the initial and boundary data. As a byproduct, one easily obtains a universal interior estimate, not depending on the parabolic data. The setting taken into account includes sourcing terms and general diffusion coefficients. The results are new, to the best of our knowledge, even in the Euclidean setting, though we treat here also the case of a complete Riemannian manifold.
2012 ◽
Vol 23
(04)
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pp. 1250009
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1995 ◽
Vol 125
(5)
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pp. 975-990
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2019 ◽
Vol 473
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pp. 297-312
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1997 ◽
Vol 127
(1)
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pp. 171-179
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2012 ◽
Vol 43
(3)
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pp. 209-232
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Vol 1
(4)
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pp. 437-464
2018 ◽
Vol 159
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pp. 511-547
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