• Corpus ID: 239024482

Schwarz symmetrizations in parabolic equations on complete manifolds

@inproceedings{Cheng2021SchwarzSI,
  title={Schwarz symmetrizations in parabolic equations on complete manifolds},
  author={Haiqing Cheng and Tengfei Ma and Kui Wang},
  year={2021}
}
  • Haiqing Cheng, Tengfei Ma, Kui Wang
  • Published 19 October 2021
  • Mathematics
In this article, we prove a sharp estimate for the solutions to parabolic equations on manifolds. Precisely, using symmetrization techniques and isoperimetric inequalities on Riemannian manifold, we obtain a Bandle’s comparison on complete noncompact manifolds with nonnegative Ricci curvature and compact manifolds with positive Ricci curvature respectively. Our results generalize Bandle’s result [6] to Riemannian setting, and Talenti’s comparison for elliptic equation on manifolds by… 

References

SHOWING 1-10 OF 25 REFERENCES
Comparison results for Poisson equation with mixed boundary condition on manifolds
  • Haiqing Cheng, Tengfei Ma, Kui Wang
  • Mathematics
  • 2021
In this article, we study Talenti’s comparison results for Poisson equation with mixed Robin boundary condition on manifolds. Precisely, using symmetrization techniques and isoperimetric
Comparison results for solutions of Poisson equations with Robin boundary on complete Riemannian manifolds
In this paper, by using Schwarz rearrangement and isoperimetric inequalities, we prove comparison results for the solutions of Poisson equations on complete Riemannian manifolds with Ric ≥ (n − 1)κ,
Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature
In this paper we consider complete noncompact Riemannian manifolds $(M, g)$ with nonnegative Ricci curvature and Euclidean volume growth, of dimension $n \geq 3$. We prove a sharp Willmore-type
Comparison results for elliptic and parabolic equations via Schwarz symmetrization
Abstract We study various extensions to general linear or nonlinear, elliptic or parabolic operators of a celebrated result due to G. Talenti. We give several comparison results for solutions of such
Moduli of Continuity for Viscosity Solutions on Manifolds
We establish the estimates of modulus of continuity for viscosity solutions of nonlinear evolution equations on manifolds, extending previous work of Andrews and Clutterbuck for regular solutions on
Comparison Results, Exit Time Moments, and Eigenvalues on Riemannian Manifolds with a Lower Ricci Curvature Bound
We study the relationship between the geometry of smoothly bounded domains in complete Riemannian manifolds and the associated sequence of $$L^1$$L1-norms of exit time moments for Brownian motion. We
Isoperimetric Comparisons via Viscosity
Viscosity solutions are suitable notions in the study of nonlinear PDEs justified by estimates established via the maximum principle or the comparison principle. Here we prove that the isoperimetric
Comparison results for solutions of nonlinear parabolic equations
We prove a comparison result for the solutions of Cauchy–Dirichlet problems for a nonlinear parabolic equation. Using Schwarz spherical symmetrization, we compare the concentration of solutions to
Neumann Problems and Steiner Symmetrization
ABSTRACT In the present paper we prove some comparison results via Steiner symmetrization for solutions to the Neumann problem where T > 0, Ω is a smooth connected open bounded subset of ℝ n , the
Metric Structures for Riemannian and Non-Riemannian Spaces
Length Structures: Path Metric Spaces.- Degree and Dilatation.- Metric Structures on Families of Metric Spaces.- Convergence and Concentration of Metrics and Measures.- Loewner Rediscovered.-
...
1
2
3
...