Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group

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 H n . Among other results, we prove that the weak solut...

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Bibliographic Details
Published in:The Journal of geometric analysis Vol. 33; no. 3; p. 77
Main Authors: Manfredini, Maria, Palatucci, Giampiero, Piccinini, Mirco, Polidoro, Sergio
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2023
Springer Nature B.V
Subjects:
Abstract Harmonic Analysis
Continuity (mathematics)
Convex and Discrete Geometry
Differential equations
Differential Geometry
Dynamical Systems and Ergodic Theory
Estimates
Fourier Analysis
Global Analysis and Analysis on Manifolds
Laplace transforms
Lie groups
Mathematics
Mathematics and Statistics
Nonlinear equations
Operators (mathematics)
Heisenberg group
Fractional sublaplacian
47G20
35B45
Quasilinear nonlocal operators
Primary 35D10
Hölder continuity
35H05
Secondary 35B05
35R05
Fractional Sobolev spaces
ISSN:1050-6926, 1559-002X
Online Access:Get full text
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Summary: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 H n . Among other results, we prove that the weak solutions to such a class of problems are bounded and Hölder continuous, by also establishing general estimates as fractional Caccioppoli-type estimates with tail and logarithmic-type estimates.
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ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-022-01124-6