Some non-standard sobolev spaces, interpolation and its application to PDE

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/16730

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor	Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.contributor.author	González Nogueras, María del Mar
dc.contributor.author	Gualdani, Maria
dc.date	2012-10
dc.identifier.citation	González, M.; Gualdani, M. Some non-standard sobolev spaces, interpolation and its application to PDE. "Acta applicandae mathematicae", Octubre 2012, vol. 121, núm. 1, p. 57-67.
dc.identifier.citation	0167-8019
dc.identifier.citation	10.1007/s10440-012-9674-6
dc.identifier.uri	http://hdl.handle.net/2117/16730
dc.language.iso	eng
dc.relation	http://www.springerlink.com/content/w228h36687847477/fulltext.pdf
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject	Functional spaces
dc.subject	Interpolation
dc.subject	Nonlinear parabolic equation
dc.subject	Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems
dc.subject	Classificació AMS::35 Partial differential equations::35S Pseudodifferential operators and other generalizations of partial differential operators
dc.subject	Classificació AMS::26 Real functions::26A Functions of one variable
dc.subject	Classificació AMS::46 Associative rings and algebras::46B Normed linear spaces and Banach spaces; Banach lattices
dc.title	Some non-standard sobolev spaces, interpolation and its application to PDE
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	We consider some nonstandard Sobolev spaces in one dimension, in which functions have different regularity in different subsets. These spaces are useful in the study of some nonlinear parabolic equations where the nonlinearity is highly degenerate and depends on the smoothness of the solution at a certain subset (that may vary with time). An example of application is a diffusion equation with a smooth free boundary, and a moving source/sink where the solution has singularity. The main new idea here is to characterize the functional space setting that is needed for semigroup theory to apply.

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