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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| Vydáno v: | The Journal of geometric analysis Ročník 33; číslo 3; s. 77 |
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01.03.2023
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| Abstract | 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. |
|---|---|
| AbstractList | 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 Hn. 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. 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 $$\mathbb {H}^n$$ 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. 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. |
| ArticleNumber | 77 |
| Author | Manfredini, Maria Polidoro, Sergio Piccinini, Mirco Palatucci, Giampiero |
| Author_xml | – sequence: 1 givenname: Maria surname: Manfredini fullname: Manfredini, Maria organization: Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia – sequence: 2 givenname: Giampiero orcidid: 0000-0002-3706-9349 surname: Palatucci fullname: Palatucci, Giampiero email: giampiero.palatucci@unipr.it organization: Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma – sequence: 3 givenname: Mirco surname: Piccinini fullname: Piccinini, Mirco organization: Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma – sequence: 4 givenname: Sergio surname: Polidoro fullname: Polidoro, Sergio organization: Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia |
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| Issue | 3 |
| Keywords | Heisenberg group Fractional sublaplacian 47G20 35B45 Quasilinear nonlocal operators Primary 35D10 Hölder continuity 35H05 Secondary 35B05 35R05 Fractional Sobolev spaces |
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