03594nam 22006375 450 991014460190332120200630030549.03-540-44885-310.1007/b12308(CKB)1000000000233094(SSID)ssj0000322328(PQKBManifestationID)11279128(PQKBTitleCode)TC0000322328(PQKBWorkID)10282317(PQKB)11044185(DE-He213)978-3-540-44885-3(MiAaPQ)EBC6297298(MiAaPQ)EBC5585864(Au-PeEL)EBL5585864(OCoLC)52371055(PPN)155182277(EXLCZ)99100000000023309420121227d2003 u| 0engurnn|008mamaatxtccrConvex Variational Problems Linear, nearly Linear and Anisotropic Growth Conditions /by Michael Bildhauer1st ed. 2003.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2003.1 online resource (XII, 220 p.) Lecture Notes in Mathematics,0075-8434 ;1818Bibliographic Level Mode of Issuance: Monograph3-540-40298-5 Includes bibliographical references (pages [207]-213) and index.1. 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.The 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.Lecture Notes in Mathematics,0075-8434 ;1818Calculus of variationsDifferential equations, PartialCalculus of Variations and Optimal Control; Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26016Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Calculus of variations.Differential equations, Partial.Calculus of Variations and Optimal Control; Optimization.Partial Differential Equations.515.64Bildhauer Michaelauthttp://id.loc.gov/vocabulary/relators/aut383383MiAaPQMiAaPQMiAaPQBOOK9910144601903321Convex variational problems145974UNINA