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    Local properties of non–negative solutions to some doubly non–linear degenerate parabolic equations

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    In the present paper we study the local behavior of non-negative weak solutions of a wide class of doubly non linear degenerate parabolic equations. We show, in particular, some lower pointwise estimates of such solutions in terms of suitable sub-potentials (dictated by the structure of the equation) and an alternative form of the Harnack inequality

    Elliptic operators with unbounded diffusion coefficients perturbed by inverse square potentials in Lp-spaces

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    In this paper we give sufficient conditions on α0\alpha \ge 0 and cRc\in \R ensuring that the space of test functions Cc(RN)C_c^\infty(\R^N) is a core for the operator L0u=(1+xα)Δu+cx2u=:Lu+cx2u,L_0u=(1+|x|^\alpha )\Delta u+\frac{c}{|x|^2}u=:Lu+\frac{c}{|x|^2}u, and L0L_0 with a suitable domain generates a quasi-contractive and positivity preserving C0C_0-semigroup in Lp(RN),1<p<L^p(\R^N),\,1<p<\infty. The proofs are based on some LpL^p-weighted Hardy's inequality and perturbation techniques
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