Interpolation Inequalities in Pattern Formation
نویسنده
چکیده
We prove some interpolation inequalities which arise in the analysis of pattern formation in physics. They are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many contexts (coarsening and branching in micromagnetics and superconductors). The main ingredient in the proof of our inequalities is a geometric construction which was first used by Choksi, Conti, Kohn, and one of the authors in [4] in the study of branching in superconductors.
منابع مشابه
Proposed Pilot Pattern Methods for Improvement DVB-T System Performance
Recently, orthogonal frequency division multiplexing (OFDM) has been extensively used in communications systems to resist channel impairments in frequency selective channels. OFDM is a multicarrier transmission technology in wireless environment that use a large number of orthogonal subcarriers to transmit information. OFDM is one of the most important blocks in digital video broadcast-terrestr...
متن کاملOne-dimensional Interpolation Inequalities, Carlson–landau Inequalities and Magnetic Schrödinger Operators
In this paper we prove refined first-order interpolation inequalities for periodic functions and give applications to various refinements of the Carlson–Landau-type inequalities and to magnetic Schrödinger operators. We also obtain Lieb-Thirring inequalities for magnetic Schrödinger operators on multi-dimensional cylinders.
متن کاملLocal and Global Interpolation Inequalities on the Folland-stein Sobolev Spaces and Polynomials on Stratified Groups
We derive both local and global Sobolev interpolation inequalities of any higher orders for the Folland-Stein Sobolev spaces on stratified nilpotent Lie groups G and on domains satisfying a certain chain condition. Weighted versions of such inequalities are also included for doubling weights satisfying a weighted Poincaré inequality. This paper appears to be the first one to deal with general S...
متن کاملSharp interpolation inequalities for discrete operators and applications
We consider interpolation inequalities for imbeddings of the l2-sequence spaces overd-dimensional lattices into the l∞ 0 spaceswritten as interpolation inequality between the l2-norm of a sequence and its difference. A general method is developed for finding sharp constants, extremal elements and correction terms in this type of inequalities. Applications to Carlson’s inequalities and spectral ...
متن کاملOptimizing design of 3D seismic acquisition by CRS trace interpolation
Land seismic data acquisition in most of cases suffers from obstacles in fields which deviates geometry of the real acquired data from what was designed. These obstacles will cause gaps, narrow azimuth and offset limitation in the data. These shortcomings, not only prevents regular trace distribution in bins, but also distorts the subsurface image by reducing illumination of the target formatio...
متن کامل