We consider nonhomogeneous, degenerate (m > 1) porous medium type equations with a nonnegative Radon measure \mu having finite total mass \mu(E_T ) on the right-hand side, and we derive linear pointwise estimates for solutions via Riesz potentials. Then, we deal with a Cauchy-Dirichlet problem for the same equation, with homogeneous boundary conditions on the parabolic boundary of the domain E_T, and we establish the existence of a solution in the sense of distributions
Porous medium type equations with measure data and potential estimates
GIANAZZA, UGO PIETRO
2013-01-01
Abstract
We consider nonhomogeneous, degenerate (m > 1) porous medium type equations with a nonnegative Radon measure \mu having finite total mass \mu(E_T ) on the right-hand side, and we derive linear pointwise estimates for solutions via Riesz potentials. Then, we deal with a Cauchy-Dirichlet problem for the same equation, with homogeneous boundary conditions on the parabolic boundary of the domain E_T, and we establish the existence of a solution in the sense of distributionsFile in questo prodotto:
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