Approximation of Free-Discontinuity Problems
Braides, Andrea.
Approximation of Free-Discontinuity Problems [electronic resource] / by Andrea Braides. - XIV, 154 p. online resource. - Lecture Notes in Mathematics, 1694 0075-8434 ; . - Lecture Notes in Mathematics, 1694 .
Functions of bounded variation -- Special functions of bounded variation -- Examples of approximation -- A general approach to approximation -- Non-local approximation.
Functionals involving both volume and surface energies have a number of applications ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations, finite-difference or non-local energies, etc.) The purpose of this book is to present a global approach to these approximations using the theory of gamma-convergence and of special functions of bounded variation. The book is directed to PhD students and researchers in calculus of variations, interested in approximation problems with possible applications.
9783540687146
10.1007/BFb0097344 doi
Differential equations, partial.
Numerical analysis.
Partial Differential Equations.
Numerical Analysis.
Theoretical, Mathematical and Computational Physics.
QA370-380
515.353
Approximation of Free-Discontinuity Problems [electronic resource] / by Andrea Braides. - XIV, 154 p. online resource. - Lecture Notes in Mathematics, 1694 0075-8434 ; . - Lecture Notes in Mathematics, 1694 .
Functions of bounded variation -- Special functions of bounded variation -- Examples of approximation -- A general approach to approximation -- Non-local approximation.
Functionals involving both volume and surface energies have a number of applications ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations, finite-difference or non-local energies, etc.) The purpose of this book is to present a global approach to these approximations using the theory of gamma-convergence and of special functions of bounded variation. The book is directed to PhD students and researchers in calculus of variations, interested in approximation problems with possible applications.
9783540687146
10.1007/BFb0097344 doi
Differential equations, partial.
Numerical analysis.
Partial Differential Equations.
Numerical Analysis.
Theoretical, Mathematical and Computational Physics.
QA370-380
515.353