Volume 27, 2021
|Number of page(s)||37|
|Published online||26 March 2021|
Global gradient estimates for nonlinear parabolic operators
Department of Mathematics and Statistics, University of Western Australia,
35 Stirling Highway,
2 Department of Mathematics, School of Science, Wuhan University of Technology, 122 Luoshi Road, 430070 Hubei, Wuhan, P.R. China.
* Corresponding author: firstname.lastname@example.org
Accepted: 4 February 2021
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.
Mathematics Subject Classification: 35B09 / 35B50 / 35K05 / 35R01
Key words: Parabolic equations on Riemannian manifolds / maximum principle / global gradient estimates
© EDP Sciences, SMAI 2021
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