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Schauder estimates for a class of fully nonlinear elliptic PDEs: a geometric tangential approach

  • Junior da Silva Bessa
  • João Vitor da Silva
  • Laura Ospina
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Abstract

In this paper, we establish local and global Schauder estimates for classical solutions of a class of fully nonlinear elliptic partial differential equations, which are not necessarily convex or concave, under suitable Hölder continuity assumptions on the data. Our approach is based on a robust blow-up argument, combined with geometric tangential analysis and compactness techniques. This strategy is strongly influenced by methodologies developed in the contemporary theory of nonlinear elliptic PDEs.

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Cite

BibTeXRIS
BibTeX
@misc{bessa2026schauder,
  title = {{Schauder estimates for a class of fully nonlinear elliptic PDEs: a geometric tangential approach}},
  author = {Junior da Silva Bessa and João Vitor da Silva and Laura Ospina},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28103},
  eprint = {2609.28103},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28103},
}
RIS
TY  - UNPB
TI  - Schauder estimates for a class of fully nonlinear elliptic PDEs: a geometric tangential approach
AU  - Junior da Silva Bessa
AU  - João Vitor da Silva
AU  - Laura Ospina
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28103
UR  - https://arxiv.org/abs/2609.28103
AB  - In this paper, we establish local and global Schauder estimates for classical solutions of a class of fully nonlinear elliptic partial differential equations, which are not necessarily convex or concave, under suitable Hölder continuity assumptions on the data. Our approach is based on a robust blow-up argument, combined with geometric tangential analysis and compactness techniques. This strategy is strongly influenced by methodologies developed in the contemporary theory of nonlinear elliptic PDEs.
ER  -