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.
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.
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.
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...
We give two examples of the generic approach to fixed point theory. The first example is concerned with the asymptotic behavior of infinite products of nonexpansive mappings in Banach spaces and the second with the existence and stability of fixed points of continuous mappings in finite-dimensional Euclidean spaces.
We establish two fixed point theorems for certain mappings of contractive type.
Let be a nonempty compact subset of a Banach space and denote by the family of all nonempty bounded closed convex subsets of . We endow with the Hausdorff metric and show that there exists a set such that its complement is -porous and such that for each and each , the set of solutions of the best approximation problem , , is nonempty and compact, and each minimizing sequence has a convergent subsequence.
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 . By examining step/terrace () surface defects it was discovered through lengthy and tedious experiments that the stored...
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