Nonsmooth Morse–Sard theorems
نویسندگان
چکیده
منابع مشابه
Tame Nonsmooth Inverse Mapping Theorems
We give several versions of local and global inverse mapping theorem for tame non necessarily smooth, mappings. Here tame mapping means a mapping which is subanalytic or, more generally, definable in some o-minimal structure. Our sufficient conditions are formulated in terms of various properties (convexity, positivity of some principal minors, contractiblity) of the space of Jacobi’s matrices ...
متن کاملNonsmooth Duality, Sandwich, and Squeeze Theorems
Given a nonlinear function h separating a convex and a concave function, we provide various conditions under which there exists an affine separating function whose graph is somewhere almost parallel to the graph of h. Such results blend Fenchel duality with a variational principle and are closely related to the Clarke–Ledyaev mean value inequality.
متن کاملMicrolocal Regularity Theorems for Nonsmooth Pseudodifferential Operators and Applications to Nonlinear Problems
The authors develop a calculus of pseudodifferential operators with nonsmooth coefficients in order to study the regularity of solutions to linear equations P(x, D)u = /. The regularity theorems are similar to those of Bony, but the calculus and the methods of proof are quite different. We apply the linear results to study the regularity properties of solutions to quasilinear partial differenti...
متن کاملInverse and Implicit Function Theorems for Nonsmooth Maps in Banach Spaces
We extend the classical inverse and implicit function theorems, the implicit function theorems of Lyusternik and Graves, and the results of Clarke and Pourciau to the situation when the given function is not smooth, but it has a convex strict prederivative whose measure of noncompactness is smaller than its measure of surjectivity. The proof of the main results requires Banach’s open mapping th...
متن کاملNonsmooth Regularization
The purpose of this paper is to present to the Inverse Problems community some recent results regarding \nonsmooth", \edge preserving" regularization methods. Emphasis is placed on the penalized least squares (Tikhonov) regularization approach with penalty functionals of total variation type, although other nonquadratic penalty functionals are brieey discussed.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinear Analysis
سال: 2017
ISSN: 0362-546X
DOI: 10.1016/j.na.2017.05.006