An interpolation approach to $L^{\infty}$ a priori estimates for elliptic problems with nonlinearity on the boundary
Analysis of PDEs
2024-05-13 v1
Abstract
We establish an explicit a priori estimate for weak solutions to subcritical elliptic problems with nonlinearity on the boundary, in terms of the powers of their norms. To prove our result, we combine in a novel way Moser type estimates together with elliptic regularity and Gagliardo--Nirenberg interpolation inequality. We illustrate our result with an application to subcritical problems satisfying Ambrosetti-Rabinowitz condition.
Keywords
Cite
@article{arxiv.2405.06304,
title = {An interpolation approach to $L^{\infty}$ a priori estimates for elliptic problems with nonlinearity on the boundary},
author = {Maya Chhetri and Nsoki Mavinga and Rosa Pardo},
journal= {arXiv preprint arXiv:2405.06304},
year = {2024}
}