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# Convex variational problems : linear, nearly linear and anisotropic growth conditions

Author: Michael Bildhauer Berlin ; New York : Springer, ©2003. Lecture notes in mathematics (Springer-Verlag), 1818. eBook : Document : EnglishView all editions and formats 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.  Read more... (not yet rated) 0 with reviews - Be the first.

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Genre/Form: Electronic books Print version:Bildhauer, Michael, 1964-Convex variational problems.Berlin ; New York : Springer, ©2003(DLC) 2003054306(OCoLC)52424019 Document, Internet resource Internet Resource, Computer File Michael Bildhauer Find more information about: Michael Bildhauer 9783540448853 3540448853 52371055 1 online resource (x, 217 pages) : illustrations. 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. Lecture notes in mathematics (Springer-Verlag), 1818. Michael Bildhauer.

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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  Read more...

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