A global differentiability result for solutions of nonlinear elliptic problems with controlled growths

Luisa Fattorusso

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This work is concerned with the inverse problem of determining initial value of the Cauchy problem for a nonlinear diffusion process with an additional condition on free boundary. Considering the flow of water through a homogeneous isotropic rigid porous medium, we have such desire: for every given positive constants $K$ and $T_{0}$ , to decide the initial value $u_{0}$ such that the solution $u (x, t)$ satisfies ${sup}_{x \in H_{u} (T_{0})} | x | \geq K$ , where $H_{u} (T_{0}) = {x \in ℝ^{N} : u (x, T_{0}) > 0}$ . In this paper, we first establish a priori estimate $u_{t} \geq C (t) u$ and a more precise Poincaré type...

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