Turnpike properties of approximate solutions of autonomous variational problems
Convergence of approximate solutions of variational problems
Structure of approximate solutions of variational problems with extended-valued convex integrands
In this work we study the structure of approximate solutions of autonomous variational problems with a lower semicontinuous strictly convex integrand : , where is the -dimensional euclidean space. We obtain a full description of the structure of the approximate solutions which is independent of the length of the interval, for all sufficiently large intervals.
A nonintersection property for extremals of variational problems with vector-valued functions
Nonoccurrence of the Lavrentiev phenomenon for nonconvex variational problems
On a variational problem arising in crystallography
We study a variational problem which was introduced by Hannon, Marcus and Mizel [ (2003) 145–149] to describe step-terraces on surfaces of so-called “unorthodox” crystals. We show that there is no nondegenerate intervals on which the absolute value of a minimizer is identically.
Structure of approximate solutions of variational problems with extended-valued convex integrands
In this work we study the structure of approximate solutions of autonomous variational problems with a lower semicontinuous strictly convex integrand : × , where is the -dimensional Euclidean space. We obtain a full description of the structure of the approximate solutions which is independent of the length of the interval, for all sufficiently large intervals.
Existence and uniform boundedness of optimal solutions of variational problems.
The turnpike property for dynamic discrete time zero-sum games.
Turnpike theorem for convex infinite dimensional discrete-time control systems.
Porosity and models with discrete innovations.
Existence of trajectories with unbounded consumption for a model with innovations.
Generic existence of solutions of nonconvex optimal control problems.
A density result in vector optimization.
A generic result in vector optimization.
Generic uniqueness of minimal configurations with rational rotation numbers in Aubry-Mather theory.
Generic uniqueness of a minimal solution for variational problems on a torus.
Existence of solutions of minimization problems with an increasing cost function and porosity.
Generic well-posedness for a class of equilibrium problems.
Anisotropic functions : a genericity result with crystallographic implications
In the 1950’s and 1960’s surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was anisotropic. By examining step/terrace (vicinal) surface defects it was discovered through lengthy and tedious experiments...
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