文摘
We consider non-homogeneous, singular (0 < m < 1) parabolic equations of porous medium type of the form $$ut - div{\kern 1pt} A\left( {x,t,u,Du} \right) = \mu {\kern 1pt} in{\kern 1pt} {E_T}$$, where ET is a space time cylinder, and µ is a Radon-measure having finite total mass µ(ET). In the range \(\frac{{\left( {N - 2} \right) + }}{N}\) < m < 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 µ.References[1]E. Acerbi and N. Fusco, Regularity for minimizers of nonquadratic functionals: the case 1 < p < 2, Journal of Mathematical Analysis and Applications 140 (1989), 115–135.MathSciNetCrossRefMATHGoogle Scholar[2]F. Bernis, J. Hulshof and J. L. Vázquez, A very singular solution for the dual porous medium equation and the asymptotic behaviour of general solutions, Journal für die Reine und Angewandte Mathematik 435 (1993), 1–31.Google Scholar[3]V. Bögelein, F. Duzaar and U. 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