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PreprintCC BY 4.0arXiv

Fractional gradients and nonlocal PDEs in variable exponent spaces

  • Susana Moura
  • Cornelia Schneider
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Abstract

We develop a theory of distributional Riesz fractional gradients in variable exponent Lebesgue spaces and introduce the associated nonlocal Sobolev spaces. Moreover, Sobolev, Hardy, Morrey, and Trudinger-type inequalities are established, and a fractional fundamental theorem of calculus is derived. As an application, we study nonlinear variational problems with nonstandard growth and establish existence and Euler--Lagrange equations for minimizers.

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Cite

BibTeXRIS
BibTeX
@misc{moura2026fractional,
  title = {{Fractional gradients and nonlocal PDEs in variable exponent spaces}},
  author = {Susana Moura and Cornelia Schneider},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08253},
  eprint = {2610.08253},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08253},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fractional gradients and nonlocal PDEs in variable exponent spaces
AU  - Susana Moura
AU  - Cornelia Schneider
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.08253
UR  - https://arxiv.org/abs/2610.08253
AB  - We develop a theory of distributional Riesz fractional gradients in variable exponent Lebesgue spaces and introduce the associated nonlocal Sobolev spaces. Moreover, Sobolev, Hardy, Morrey, and Trudinger-type inequalities are established, and a fractional fundamental theorem of calculus is derived. As an application, we study nonlinear variational problems with nonstandard growth and establish existence and Euler--Lagrange equations for minimizers.
ER  -