Positive solutions of -Δu=f(u) with f(s)=s^{2*-1}L(s), L slowly varying and satisfying a derivative-decay condition, have a uniform L∞ bound independent of the solution.
Pardo.L∞(Ω) a priori estimates for subcritical semilinear elliptic equations with a Carathéodory non-linearity.J
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Uniform a priori bounds for Slightly Subcritical Elliptic Problems
Positive solutions of -Δu=f(u) with f(s)=s^{2*-1}L(s), L slowly varying and satisfying a derivative-decay condition, have a uniform L∞ bound independent of the solution.