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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Parabolic Equations in Anisotropic Orlicz Spaces with General N-functions
verfasst von : Piotr Gwiazda, Agnieszka Świerczewska Gwiazda
Erschienen in: Parabolic Problems
Verlag: Springer Basel
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In the present paper we study the existence of weak solutions to an abstract parabolic initial-boundary value problem. On the operator appearing in the equation we assume the coercivity conditions given by an
N
-function (i.e., convex function satisfying conditions specified in the paper). The main novelty of the paper consists in the lack of any growth restrictions on the
N
-function combined with an anisotropic character of the
N
-function, namely we allow the dependence on all the directions of the gradient, not only on its absolute value.