Abstract
On a cylindrical domain E_T, we consider doubly nonlinear parabolic equations, whose prototype is partial _t u - mathrm{div}(|u|^{m-1}|Du|^{p-2}Du) = mu , where mu is a non-negative Radon measure having finite total mass mu (E_T). The central objective is to establish pointwise estimates for weak solutions in terms of nonlinear parabolic potentials in the doubly degenerate case (pge 2, m>1). Moreover, we will prove the sharpness of the estimates by giving an optimal Lorentz space criterion regarding the local uniform boundedness of weak solutions and by comparing them to the decay of the Barenblatt solution.
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