On the pointwise Schauder estimates for elliptic equations
Igor Kukavica, Quinn Le
TL;DR
This paper extends pointwise Schauder estimates for elliptic and parabolic equations to a broader range of Lp exponents, enhancing understanding of regularity in elliptic PDEs.
Contribution
It generalizes existing Schauder estimates to include the full range of Lp exponents between 1 and n/m for elliptic and parabolic equations.
Findings
Extended Schauder estimates to 1 < p < n/m range
Provided new pointwise regularity results for elliptic equations
Enhanced understanding of Lp regularity in PDEs
Abstract
We consider the pointwise in space Lp-type regularity for elliptic and parabolic equations of order m in Rn. We provide pointwise Schauder estimates for the general range of Lp exponents, extending previous results from p > n/m to 1 < p < n/m.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Advanced Harmonic Analysis Research