Equivalence between uniform $L^{2^\star}(\Omega)$ a-priori bounds and uniform $L^{\infty}(\Omega)$ a-priori bounds for subcritical elliptic equations

Alfonso Castro, Nsoki Mavinga, Rosa Pardo

DOI: http://dx.doi.org/10.12775/TMNA.2018.036

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.

Keywords


A priori estimates; positive solutions; subcritical nonlinearity; radial solutions

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