Interior and up to the boundary regularity for the fractional $g$-Laplacian: the convex case

Ariel Salort; Hern\'an Vivas; Juli\'an Fern\'andez Bonder

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Interior and up to the boundary regularity for the fractional $g$-Laplacian: the convex case

Julián Fernández Bonder, Ariel Salort, Hernán Vivas

Analysis of PDEs · Submitted 12 Aug 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We establish interior and up to the boundary H\"older regularity estimates for weak solutions of the Dirichlet problem for the fractional $g-$Laplacian with bounded right hand side and $g$ convex.

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arXiv ID2008.05543 (version 4)

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CitationAriel Salort, Hern\'an Vivas, Juli\'an Fern\'andez Bonder. "Interior and up to the boundary regularity for the fractional $g$-Laplacian: the convex case." arXiv:2008.05543 (2020). https://pith.science/paper/IC5N7FKT

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We establish interior and up to the boundary H\"older regularity estimates for weak solutions of the Dirichlet problem for the fractional $g-$Laplacian with bounded right hand side and $g$ convex. These are the first regularity results available in the literature for integro-differential equations in the context of fractional Orlicz-Sobolev spaces.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We establish interior and up to the boundary H\"older regularity estimates for weak solutions of the Dirichlet problem for the fractional $g-$Laplacian with bounded right hand side and $g$ convex.	result 0.75	0.96	0.95	asserted 1.00
s1	These are the first regularity results available in the literature for integro-differential equations in the context of fractional Orlicz-Sobolev spaces.	gap 0.59	0.35	0.10	asserted 1.00

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Original abstract

We establish interior and up to the boundary H\"older regularity estimates for weak solutions of the Dirichlet problem for the fractional $g-$Laplacian with bounded right hand side and $g$ convex. These are the first regularity results available in the literature for integro-differential equations in the context of fractional Orlicz-Sobolev spaces.

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11 arXiv papers cite this in 12 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 5 sentences without a confident label

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The present paper is substantially different from [ref] .

Regularity for nonlocal problems with non-standard growth · Introduction · 1.00

Cites it as background 6 papers

As far as we know, first regularity results for fractional order Orlicz–Sobolev spaces have been proved in [ref] by Fernández Bonder, Salort and Vivas.

Regularity for nonlocal problems with non-standard growth · Introduction · 0.94
On the other hand, Fernández Bonder-Salort-Vivas [ref] established the Hölder continuity for weak solutions to the fractional $g$-Laplacian with Dirichlet boundary values; see also [ref] for the global regularity of eigenfunctions.

Harnack inequality for the nonlocal equations with general growth · Introduction · 0.89
For more details on the fractional Orlicz-Sobolev spaces, we refer the reader to [ref] and the references therein.

Ground state and nodal solutions for fractional Orlicz problems with lack of regularity and without the Ambrosetti-Rabinowitz condition · Introduction · 1.00

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Uses the method or tool of 1 paper

Now, we use ellipticity and the fact that [equation] to get [equation] Therefore $I$ can be bound exactly as the second term of (3.6) in [ref] .

Global H\"older regularity for the fractional $p$-Laplacian · Boundary behavior · 0.87

Cites as background 4 papers

These spaces have received a great amount of attention in the last years, either in the study of their structural properties [ref] or the PDE questions that arise such as eigenvalue problems [ref] and Pólya-Szegö type results [ref] .

Fractional Orlicz-Sobolev embeddings · Introduction and main results · 0.98
These spaces have received a great amount of attention in the last years, either in the study of their structural properties [ref] or the PDE questions that arise such as eigenvalue problems [ref] and Pólya-Szegö type results [ref] .

On the limit as $s\to 0^+$ of fractional Orlicz-Sobolev spaces · Introduction and main results · 0.98
These spaces have received a great amount of attention in the last years, either in the study of their structural properties [ref] or the PDE questions that arise such as eigenvalue problems [ref] and Pólya-Szegö type results [ref] .

Fractional eigenvalues in Orlicz spaces with no $\Delta_2$ condition · Introduction and main results · 0.98

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