We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the validity of the estimates in the global domain, and it detects several additional regularity effects due to special parabolic data. Moreover, our result comprises a large number of nonlinear sources treated by a unified approach, and it recovers many classical results as special cases.
Global Gradient Estimates for a General Type of Nonlinear Parabolic Equations / C. Cavaterra, S. Dipierro, Z. Gao, E. Valdinoci. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 32:2(2022 Feb), pp. 65.1-65.37. [10.1007/s12220-021-00812-z]
Global Gradient Estimates for a General Type of Nonlinear Parabolic Equations
C. Cavaterra;
2022
Abstract
We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the validity of the estimates in the global domain, and it detects several additional regularity effects due to special parabolic data. Moreover, our result comprises a large number of nonlinear sources treated by a unified approach, and it recovers many classical results as special cases.
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Cavaterra2022_Article_GlobalGradientEstimatesForAGen(1).pdf
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