| Abstract: |
| In this talk, we present an explicit $L^{\infty}(\Omega)$ estimate for weak solutions to subcritical elliptic problems with nonlinearity on the boundary, expressed in terms of powers of their $H^1(\Omega)$ norm. Our approach relies on the already available regularity results, established using Moser's iteration technique, elliptic regularity and Gagliardo–Nirenberg interpolation inequality. We illustrate our result with an application to subcritical problems satisfying Ambrosetti-Rabinowitz condition. |
|