Global sharp gradient estimates for a nonlinear parabolic equation on Riemannian manifolds
-
Le Huy Chuan
and
Nguyen Tien Manh
Abstract
In this paper, we employ the techniques in [C. Cavaterra, S. Dipierro, Z. Gao and E. Valdinoci, Global gradient estimates for a general type of nonlinear parabolic equations, J. Geom. Anal. 32 2022, 2, Paper No. 65] and the approach in [H. T. Dung and N. T. Dung, Sharp gradient estimates for a heat equation in Riemannian manifolds, Proc. Amer. Math. Soc. 147 2019, 12, 5329–5338] to derive sharp gradient estimates for a positive solution to the heat equation
in a complete noncompact Riemannian manifold (where a is a real constant). This is an extension of the gradient estimates of Dung and Dung.
Funding source: VNU Science and Technology Development Fund
Award Identifier / Grant number: TN.23.03
Funding statement: Nguyen Tien Manh is supported by the project “Gradient estimate for nonlinear parabolic type equations on manifolds” under grant number TN.23.03. He would like to express his thanks to VNU – University of Science in Hanoi for financial support.
References
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Gronwall type inequality on generalized fractional conformable integral operators
- Asymptotic modelling of viscoelastic von Kármán membrane shells
- Global sharp gradient estimates for a nonlinear parabolic equation on Riemannian manifolds
- Scattering of an inhomogeneous coupled Schrödinger system in the conformal space
- Existence of non-negative periodic solutions for a degenerate anisotropic parabolic equation with strongly nonlinear source
- Fractional integral inequalities for the s-(κ,H)-convex function
- Some properties of Ψ-gamma, Ψ-beta and Ψ-hypergeometric matrix functions
- On the fractional q-integral operators involving q-analogue of Mittag-Leffler function
Articles in the same Issue
- Frontmatter
- Gronwall type inequality on generalized fractional conformable integral operators
- Asymptotic modelling of viscoelastic von Kármán membrane shells
- Global sharp gradient estimates for a nonlinear parabolic equation on Riemannian manifolds
- Scattering of an inhomogeneous coupled Schrödinger system in the conformal space
- Existence of non-negative periodic solutions for a degenerate anisotropic parabolic equation with strongly nonlinear source
- Fractional integral inequalities for the s-(κ,H)-convex function
- Some properties of Ψ-gamma, Ψ-beta and Ψ-hypergeometric matrix functions
- On the fractional q-integral operators involving q-analogue of Mittag-Leffler function
