| Abstract: |
| In this talk, we present an explicit $L^\infty(\Omega)$ a priori estimate for weak solutions to semilinear elliptic equations with nonlinearity on the boundary, in terms of the powers of their $H^1(\Omega)$ norms. We combine an appropriate version of a Moser iteration argument along with elliptic regularity and Gagliardo--Nirenberg interpolation inequality to prove our result. We illustrate our result with an application to subcritical problems satisfying Ambrosetti-Rabinowitz condition. |
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