Local Minimization, Variational Evolution and Γ-Convergence
Braides, Andrea.
Local Minimization, Variational Evolution and Γ-Convergence [electronic resource] / by Andrea Braides. - XI, 174 p. 42 illus. online resource. - Lecture Notes in Mathematics, 2094 0075-8434 ; . - Lecture Notes in Mathematics, 2094 .
Introduction -- Global minimization -- Parameterized motion driven by global minimization -- Local minimization as a selection criterion -- Convergence of local minimizers -- Small-scale stability -- Minimizing movements -- Minimizing movements along a sequence of functionals -- Geometric minimizing movements -- Different time scales -- Stability theorems -- Index.
This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.
9783319019826
10.1007/978-3-319-01982-6 doi
Mathematics.
Differential equations, partial.
Mathematical optimization.
Global analysis (Mathematics).
Functional analysis.
Applications of Mathematics.
Partial Differential Equations.
Calculus of Variations and Optimal Control; Optimization.
Approximations and Expansions.
Analysis.
Functional Analysis.
T57-57.97
519
Local Minimization, Variational Evolution and Γ-Convergence [electronic resource] / by Andrea Braides. - XI, 174 p. 42 illus. online resource. - Lecture Notes in Mathematics, 2094 0075-8434 ; . - Lecture Notes in Mathematics, 2094 .
Introduction -- Global minimization -- Parameterized motion driven by global minimization -- Local minimization as a selection criterion -- Convergence of local minimizers -- Small-scale stability -- Minimizing movements -- Minimizing movements along a sequence of functionals -- Geometric minimizing movements -- Different time scales -- Stability theorems -- Index.
This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.
9783319019826
10.1007/978-3-319-01982-6 doi
Mathematics.
Differential equations, partial.
Mathematical optimization.
Global analysis (Mathematics).
Functional analysis.
Applications of Mathematics.
Partial Differential Equations.
Calculus of Variations and Optimal Control; Optimization.
Approximations and Expansions.
Analysis.
Functional Analysis.
T57-57.97
519