Convex Variational Problems
Bildhauer, Michael.
Convex Variational Problems Linear, Nearly Linear and Anisotropic Growth Conditions / [electronic resource] : by Michael Bildhauer. - XII, 220 p. online resource. - Lecture Notes in Mathematics, 1818 0075-8434 ; . - Lecture Notes in Mathematics, 1818 .
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 $-elliptic integrands -- 5. Bounded solutions for convex variational problems with a wide range of anisotropy -- 6. Anisotropic linear/superlinear growth in the scalar case -- A. Some remarks on relaxation -- B. Some density results -- C. Brief comments on steady states of generalized Newtonian fluids -- D. Notation and conventions -- References -- Index.
The author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions. This volume first focuses on elliptic variational problems with linear growth conditions. Here the notion of a "solution" is not obvious and the point of view has to be changed several times in order to get some deeper insight. Then the smoothness properties of solutions to convex anisotropic variational problems with superlinear growth are studied. In spite of the fundamental differences, a non-uniform ellipticity condition serves as the main tool towards a unified view of the regularity theory for both kinds of problems.
9783540448853
10.1007/b12308 doi
Mathematical optimization.
Differential equations, partial.
Calculus of Variations and Optimal Control; Optimization.
Partial Differential Equations.
QA315-316 QA402.3 QA402.5-QA402.6
515.64
Convex Variational Problems Linear, Nearly Linear and Anisotropic Growth Conditions / [electronic resource] : by Michael Bildhauer. - XII, 220 p. online resource. - Lecture Notes in Mathematics, 1818 0075-8434 ; . - Lecture Notes in Mathematics, 1818 .
1. Introduction -- 2. Variational problems with linear growth: the general setting -- 3. Variational integrands with ($,\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.
9783540448853
10.1007/b12308 doi
Mathematical optimization.
Differential equations, partial.
Calculus of Variations and Optimal Control; Optimization.
Partial Differential Equations.
QA315-316 QA402.3 QA402.5-QA402.6
515.64