An Interpolation Approach To L∞ A Priori Estimates For Elliptic Problems With Nonlinearity On The Boundary
Document Type
Article
Publication Date
2-14-2025
Published In
Proceedings Of The American Mathematical Society
Abstract
We establish an explicit L∞(Ω) a priori estimate for weak solutions to subcritical elliptic problems with nonlinearity on the boundary, in terms of the powers of their 𝐻¹(Ω) 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.
Recommended Citation
M. Chhetri, Nsoki Mavinga, and R. Pardo.
(2025).
"An Interpolation Approach To L∞ A Priori Estimates For Elliptic Problems With Nonlinearity On The Boundary".
Proceedings Of The American Mathematical Society.
Volume 153,
Issue 4.
1585-1593.
DOI: 10.1090/proc/17075
https://works.swarthmore.edu/fac-math-stat/332