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100   $a20121227d2003      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aConvex Variational Problems $eLinear, nearly Linear and Anisotropic Growth Conditions /$fby Michael Bildhauer
205   $a1st ed. 2003.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2003.
215   $a1 online resource (XII, 220 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1818
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-40298-5 
320   $aIncludes bibliographical references (pages [207]-213) and index.
327   $a1. Introduction -- 2. Variational problems with linear growth: the general setting -- 3. Variational integrands with ($,\mu ,q$)-growth -- 4. Variational problems with linear growth: the case of $\mu $-elliptic integrands -- 5. Bounded solutions for convex variational problems with a wide range of anisotropy -- 6. Anisotropic linear/superlinear growth in the scalar case -- A. Some remarks on relaxation -- B. Some density results -- C. Brief comments on steady states of generalized Newtonian fluids -- D. Notation and conventions -- References -- Index.
330   $aThe author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions. This volume first focuses on elliptic variational problems with linear growth conditions. Here the notion of a "solution" is not obvious and the point of view has to be changed several times in order to get some deeper insight. Then the smoothness properties of solutions to convex anisotropic variational problems with superlinear growth are studied. In spite of the fundamental differences, a non-uniform ellipticity condition serves as the main tool towards a unified view of the regularity theory for both kinds of problems.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1818
606   $aCalculus of variations
606   $aDifferential equations, Partial
606   $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
615  0$aCalculus of variations.
615  0$aDifferential equations, Partial.
615 14$aCalculus of Variations and Optimal Control; Optimization.
615 24$aPartial Differential Equations.
676   $a515.64
700   $aBildhauer$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut$0383383
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910144601903321
996   $aConvex variational problems$9145974
997   $aUNINA