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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.
##### MSC:
 35B65 Smoothness and regularity of solutions to PDEs 35J60 Nonlinear elliptic equations 35J20 Variational methods for second-order elliptic equations
##### Keywords:
removable singularity
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##### References:
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