We consider non-homogeneous, singular (m\in(0,1)) parabolic equations of porous medium type of the form u_t−div A(x,t,u,Du)=\mu\qquad in E_T, where E_T is a space time cylinder, and \mu is a Radon-measure having finite total mass \mu(E_T). In the range m\in((N−2)+/N,1) we establish sufficient conditions for the boundedness and the continuity of u in terms of a natural Riesz potential of the right-hand side measure \mu.
Sharp boundedness and continuity results for the singular porous medium equation
GIANAZZA, UGO PIETRO
2016-01-01
Abstract
We consider non-homogeneous, singular (m\in(0,1)) parabolic equations of porous medium type of the form u_t−div A(x,t,u,Du)=\mu\qquad in E_T, where E_T is a space time cylinder, and \mu is a Radon-measure having finite total mass \mu(E_T). In the range m\in((N−2)+/N,1) we establish sufficient conditions for the boundedness and the continuity of u in terms of a natural Riesz potential of the right-hand side measure \mu.File in questo prodotto:
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