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Regularity and uniqueness results in grand Sobolev spaces for parabolic equations with measure data. (English) Zbl 1007.35034

It is considered the Cauchy-Dirichlet problem for the operator \(\partial_tu-\Delta_Nu=\mu\), where \(\mu\in L^1(0,T;M(\Omega))\) and the initial data belongs to the space of the Radon measures \(M(\Omega).\) There are extended some existence and uniqueness results in Sobolev spaces to the case of grand Sobolev spaces.

MSC:

35K20 Initial-boundary value problems for second-order parabolic equations
35R05 PDEs with low regular coefficients and/or low regular data
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35D05 Existence of generalized solutions of PDE (MSC2000)
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