Fiorenza, Alberto; Mercaldo, Anna; Rakotoson, Jean Michel Regularity and uniqueness results in grand Sobolev spaces for parabolic equations with measure data. (English) Zbl 1007.35034 Discrete Contin. Dyn. Syst. 8, No. 4, 893-906 (2002). 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. Reviewer: Lubomira Softova (Bari) Cited in 17 Documents 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) Keywords:Cauchy-Dirichlet problem; Radon measures PDFBibTeX XMLCite \textit{A. Fiorenza} et al., Discrete Contin. Dyn. Syst. 8, No. 4, 893--906 (2002; Zbl 1007.35034) Full Text: DOI