The Porous Medium Equation with Measure Data
نویسنده
چکیده
We study the existence of solutions to the porous medium equation with a nonnegative, finite Radon measure on the right hand side. We show that such problems have solutions in a wide class of supersolutions. These supersolutions are defined as lower semicontinuous functions obeying a parabolic comparison principle with respect to continuous solutions. We also consider the question of how the integrability of the gradient of solutions is affected if the measure is given by a function in L, for a small exponent s > 1.
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