Sobolev contractivity of gradient flow maximal functions
-
Simon Bortz
und
Olli Saari
Abstract
We prove that the energy dissipation property of gradient flows extends to semigroup maximal operators in various settings. In particular, we show that the vertical maximal function relative to the p-parabolic extension does not increase the p-norm of the gradient when
Funding source: Simons Foundation
Award Identifier / Grant number: 959861
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: 390685813
Award Identifier / Grant number: 211504053
Funding statement: This research was supported by the CNRS through the second author’s PEPS JCJC project. The first author is funded by the Simons Foundation Travel Support for Mathematicians Grant number 959861. The third author was funded by the Deutsche Forschungsgemeinschaft under project numbers 390685813 (EXC 2047: Hausdorff Center for Mathematics) and 211504053 (CRC 1060: Mathematics of Emergent Effects).
Acknowledgements
The authors would like to thank Katharina Egert for tolerating their persistent presence for the better part of two weeks (and longer in the case of the second named author). The authors are grateful to an anonymous referee for valuable comments and for suggesting a simpler proof of Lemma 3.14.
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Another proof of the existence of homothetic solitons of the inverse mean curvature flow
- A Weierstrass extremal field theory for the fractional Laplacian
- Minimizing movements for anisotropic and inhomogeneous mean curvature flows
- A singular Yamabe problem on manifolds with solid cones
- Uniqueness for volume-constraint local energy-minimizing sets in a half-space or a ball
- Limit of solutions for semilinear Hamilton–Jacobi equations with degenerate viscosity
- Monotonicity of entire solutions to reaction-diffusion equations involving fractional p-Laplacian
- Hierarchy structures in finite index CMC surfaces
- No breathers theorem for noncompact harmonic Ricci flows with asymptotically nonnegative Ricci curvature
- Wolff potentials and local behavior of solutions to elliptic problems with Orlicz growth and measure data
- Asymptotic analysis of single-slip crystal plasticity in the limit of vanishing thickness and rigid elasticity
- On the regularity of optimal potentials in control problems governed by elliptic equations
- Sobolev embeddings and distance functions
- Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure: The limiting regimes
- On the area-preserving Willmore flow of small bubbles sliding on a domain’s boundary
- Sobolev contractivity of gradient flow maximal functions
- Discrete approximation of nonlocal-gradient energies
- Symmetry and monotonicity of singular solutions to p-Laplacian systems involving a first order term
- Flat flow solution to the mean curvature flow with volume constraint
Artikel in diesem Heft
- Frontmatter
- Another proof of the existence of homothetic solitons of the inverse mean curvature flow
- A Weierstrass extremal field theory for the fractional Laplacian
- Minimizing movements for anisotropic and inhomogeneous mean curvature flows
- A singular Yamabe problem on manifolds with solid cones
- Uniqueness for volume-constraint local energy-minimizing sets in a half-space or a ball
- Limit of solutions for semilinear Hamilton–Jacobi equations with degenerate viscosity
- Monotonicity of entire solutions to reaction-diffusion equations involving fractional p-Laplacian
- Hierarchy structures in finite index CMC surfaces
- No breathers theorem for noncompact harmonic Ricci flows with asymptotically nonnegative Ricci curvature
- Wolff potentials and local behavior of solutions to elliptic problems with Orlicz growth and measure data
- Asymptotic analysis of single-slip crystal plasticity in the limit of vanishing thickness and rigid elasticity
- On the regularity of optimal potentials in control problems governed by elliptic equations
- Sobolev embeddings and distance functions
- Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure: The limiting regimes
- On the area-preserving Willmore flow of small bubbles sliding on a domain’s boundary
- Sobolev contractivity of gradient flow maximal functions
- Discrete approximation of nonlocal-gradient energies
- Symmetry and monotonicity of singular solutions to p-Laplacian systems involving a first order term
- Flat flow solution to the mean curvature flow with volume constraint
