Abstract
We provide sufficient conditions for a uniform $L^{2^\star}(\Omega)$ bound to imply a uniform $L^\infty (\Omega)$ bound for positive classical solutions to a class of subcritical elliptic problems in bounded $C^2$ domains in $\mathbb R^N$. We also establish an equivalent result for sequences of boundary value problems.
Citation
Alfonso Castro. Nsoki Mavinga. Rosa Pardo. "Equivalence between uniform $L^{2^\star}(\Omega)$ a-priori bounds and uniform $L^{\infty}(\Omega)$ a-priori bounds for subcritical elliptic equations." Topol. Methods Nonlinear Anal. 53 (1) 43 - 56, 2019. https://doi.org/10.12775/TMNA.2018.036