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Elliptic and parabolic problems in unbounded domains
Authors:Patrick Guidotti
Abstract:We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi‐explicit representation formulas via operator‐valued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the large, singular perturbations, exact boundary conditions on artificial boundaries and validity of maximum principles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Keywords:Elliptic and parabolic problems  semi‐classical fundamental solutions  regularity theory  maximum principle  asymptotic behavior  singular perturbation  artificial boundary conditions
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