Continuity results for solutions of certain degenerate parabolic equations
Giulia Sargenti (1998)
Rendiconti del Seminario Matematico della Università di Padova
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Giulia Sargenti (1998)
Rendiconti del Seminario Matematico della Università di Padova
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Dominique Blanchard, Alessio Porretta (2001)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Francis Ribaud (1998)
Revista Matemática Iberoamericana
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We study local and global Cauchy problems for the Semilinear Parabolic Equations ∂U - ΔU = P(D) F(U) with initial data in fractional Sobolev spaces H (R). In most of the studies on this subject, the initial data U(x) belongs to Lebesgue spaces L(R) or to supercritical fractional Sobolev spaces H (R) (s > n/p). Our purpose is to study the intermediate cases (namely for 0 < s < n/p). We give some mapping properties for functions with polynomial...
Andrea Dall&#039;Aglio, François Murat (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Abderrahmane El Hachimi, François De Thélin (1991)
Publicacions Matemàtiques
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In this paper we consider a nonlinear parabolic equation of the following type: (P) ∂u/∂t - div(|∇p|p-2 ∇u) = h(x,u) with Dirichlet boundary conditions and initial data in the case when 1 < p < 2. We construct supersolutions of (P), and by use of them, we prove that for tn → +∞, the solution of (P) converges to some solution of the elliptic equation associated with...
D. G. Aronson, James Serrin (1967)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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José C. Fernandes, Bruno Franchi (1996)
Revista Matemática Iberoamericana
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It is known that degenerate parabolic equations exhibit somehow different phenomena when we compare them with their elliptic counterparts. Thus, the problem of existence and properties of the Green function for degenerate parabolic boundary value problems is not completely solved, even after the contributions of [GN] and [GW4], in the sense that the existence problem is still open, even if the a priori estimates proved in [GN] will be crucial in our approach (...).