JournalsrlmVol. 32, No. 2pp. 213–231

Radon measure-valued solutions of quasilinear parabolic equations

  • Alberto Tesei

    Università Sapienza di Roma and Istituto per le Applicazioni del Calcolo ‘‘M. Picone’’, Roma, Italy
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Abstract

We discuss some recent results concerning Radon measure-valued solutions of the Cauchy–Dirichlet problem for tu=Δϕ(u)\partial_t u = \Delta\phi(u). The function ϕ\phi is continuous, nondecreasing, with a growth at most powerlike. Well-posedness and regularity results are described, which depend on whether the initial data charge sets of suitable capacity (determined both by the Laplacian and by the growth order of ϕ\phi), and on suitable compatibility conditions at ±\pm\infty.

Cite this article

Alberto Tesei, Radon measure-valued solutions of quasilinear parabolic equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 32 (2021), no. 2, pp. 213–231

DOI 10.4171/RLM/934