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Regularity of the extremal solution for a biharmonic problem with general nonlinearity

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  • We consider the class of radial solutions of semilinear equations $\Delta^2 u=\lambda f(u)$ in the unit ball of $\mathbb R^N$. It is the class of stable solutions which includes minimal solutions and extremal solution. We establish the regularity of this extremal solution for $N\leq 9$. Our regularity results do not depend on the specific nonlinearity $f$.
    Mathematics Subject Classification: Primary: 31B30; Secondary: 74B0.

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