Annales Academię Scientiarum Fennicę
Mathematica
Volumen 34, 2009, 583-605

INITIAL-BOUNDARY VALUE PROBLEMS FOR PARABOLIC EQUATIONS

Magnus Fontes

Lund University, Centre for Mathematical Sciences
Box 118, SE-221 00 Lund, Sweden; fontes 'at' maths.lth.se

Abstract. We prove new existence and uniqueness results for weak solutions to non-homogeneous initial-boundary value problems for parabolic equations modeled on the evolution of the p-Laplacian.

2000 Mathematics Subject Classification: Primary 35K60, 35K55.

Key words: Parabolic equations, nonhomogeneous boundary conditions, nonhomogeneous initial data, Hilbert transform, anisotropic Sobolev spaces, evolution of p-Laplacian.

Reference to this article: M. Fontes: Initial-boundary value problems for parabolic equations. Ann. Acad. Sci. Fenn. Math. 34 (2009), 583-605.

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