Existence of Minimizers for NonLevel Convex Supremal Functionals
نویسندگان
چکیده
The paper is devoted to determine necessary and sufficient conditions for existence of solutions to the problem inf { ess sup x∈Ω f(∇u(x)) : u ∈ u0 +W 1,∞ 0 (Ω) } , when the supremand f is not necessarily level convex. These conditions are obtained through a comparison with the related level convex problem and are written in terms of a differential inclusion involving the boundary datum. Several conditions of convexity for the supremand f are also investigated.
منابع مشابه
Minimizers for a Double-well Problem with Affine Boundary Conditions
This paper is concerned with the existence of minimizers for functionals having a double-well integrand with affine boundary conditions. Such functionals are related to the so-called Kohn-Strang functional which arises in optimal shape design problems in electrostatics or elasticity. They are known to be not quasi-convex, and therefore existence of minimizers is, in general, guaranteed only for...
متن کاملEXISTENCE AND REGULARITY OF MINIMIZERS OF NONCONVEX INTEGRALS WITH p− q GROWTH
We show that local minimizers of functionals of the form Z Ω [f(Du(x)) + g(x , u(x))] dx, u ∈ u0 + W 1,p 0 (Ω), are locally Lipschitz continuous provided f is a convex function with p − q growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional.
متن کاملCharacterization of Minimizers of Convex Regularization Functionals
We study variational methods of bounded variation type for the data analysis. Y. Meyer characterized minimizers of the Rudin-Osher-Fatemi functional in dependence of the G-norm of the data. These results and the follow up work on this topic are generalized to functionals defined on spaces of functions with derivatives of finite bounded variation. In order to derive a characterization of minimiz...
متن کاملGeneralized minimizers of convex integral functionals, Bregman distance, Pythagorean identities
Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The integrands are finite on the positive and infinite on the negative numbers, strictly convex but not necessarily differentiable. The minimization is viewed as a primal problem and studied together with a dual one in the framework of convex duality. The effective domain of the val...
متن کاملMinimizers of Convex Functionals Arising in Random Surfaces
We investigate C1 regularity of minimizers to ́ F (∇u)dx in two dimensions for certain classes of non-smooth convex functionals F . In particular our results apply to the surface tensions that appear in recent works on random surfaces and random tilings of Kenyon, Okounkov and others.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Control and Optimization
دوره 52 شماره
صفحات -
تاریخ انتشار 2014