H\'older continuity and boundedness estimates for nonlinear fractional equations in the Heisenberg group
| Autor: | Manfredini, Maria, Palatucci, Giampiero, Piccinini, Mirco, Polidoro, Sergio |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional $p$-Laplacian operator on the Heisenberg-Weyl group $\mathbb{H}^n$. Amongst other results, we prove that the weak solutions to such a class of problems are bounded and H\"older continuous, by also establishing general estimates as fractional Caccioppoli-type estimates with tail and logarithmic-type estimates. Comment: We have removed the bound on the integrability exponent p. To appear in J. Geom. Anal |
| Databáze: | arXiv |
| Externí odkaz: |
|