Sobolev contractivity of gradient flow maximal functions
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 p > 2 . We also obtain anal...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/398730 |
| Acceso en línea: | https://hdl.handle.net/2117/398730 https://dx.doi.org/10.1515/acv-2023-0026 |
| Access Level: | acceso abierto |
| Palabra clave: | Sobolev gradients Regularity of maximal functions Gradient flow Sobolev, Gradients de Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems Classificació AMS::42 Fourier analysis::42B Fourier analysis in several variables Classificació AMS::43 Abstract harmonic analysis Classificació AMS::47 Operator theory::47J Equations and inequalities involving nonlinear operators |
| Sumario: | 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 p > 2 . We also obtain analogous results in the setting of uniformly parabolic and elliptic equations with bounded, measurable, real and symmetric coefficients. These are the first regularity results for vertical maximal functions without convolution structure. |
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