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A priori regularity for weak solutions of some nonlinear elliptic equations. (English) Zbl 0837.35027
Summary: Let \(f(u)\) be some positive regular function bounded from above by \(u^{{n\over n-2}}\), in \(\mathbb{R}^+\). We derive some necessary and sufficient conditions, in order for all positive solutions to \(- \Delta u= f(u)\in L^1_{\text{loc}}(\mathbb{R}^n)\) to be regular.
35B65 Smoothness and regularity of solutions to PDEs
35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
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