$q$-Moment Estimates for the Singular $p$-Laplace Equation and Applications
- Authors
- Liming Yin and Samuel Drapeau
- Date
- 2021
- Journal
- Nonlinear Analysis, 211
- Abstract
- We provide $q$-moment estimates on annuli for weak solutions of the singular $p$-Laplace equation where $p$ and $q$ are conjugates. We derive $q$-uniform integrability for some critical parameter range. As a application, we derive a mass conservation as well as a weak convergence result for a larger critical parameter range. Concerning the latter point, we further provide a rate of convergence of order $t^{q−1}$ of the solution in the $q$-Wasserstein distance.
- Keywords
- Singular $p$-Laplace Equation, Moment Estimates, Mass Conservation, Convergence Rate in Wasserstein Distance
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