Antonio M. Greco, Giovanni Porru
Abstract
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We investigate explosive solutions of the equation $\Delta u=f(u)$ in a bounded convex domain $D$. We find some asymptotic estimates and prove the log-convexity of the solution $u(x)$ under suitable conditions on $f$.
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We investigate explosive solutions of the equation $\Delta u=f(u)$ in a bounded convex domain $D$. We find some asymptotic estimates and prove the log-convexity of the solution $u(x)$ under suitable conditions on $f$.
Key concepts: Convexity, Mathematics, Bounded function, Domain (mathematical analysis), Explosive material, Regular polygon, Convex domain, Applied mathematics