منابع مشابه
Inequalities Relating Critical Exponents
During modern era of critical phenomena, several inequalities between critical exponents have been derived. However most of these inequalities depend on some assumptions. Beside this, some of these inequalities can be replaced by equalities. Several solved classical models as well as some recent theories have helped us to check the validity of these inequalities. To check these inequalities in ...
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Abstract We consider Hardy inequalities in IRn, n ≥ 3, with best constant that involve either distance to the boundary or distance to a surface of co-dimension k < n, and we show that they can still be improved by adding a multiple of a whole range of critical norms that at the extreme case become precisely the critical Sobolev norm. Résumé Nous étudions des inegalités de Hardy dans IRn, n ≥ 3,...
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A purpose of critical point theory is the counting of critical points of functions. Principal theorems in the subject state in precise terms that topological complexity of the underlying space is reflected in the existence and nature of critical points of any smooth real-valued function defined on the space. The initial development of critical point theory is peculiarly the work of one man, Mar...
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Similar evolutionary variational inequalities appear as convenient formulations for continuous quasistationary models for sandpile growth, formation of a network of lakes and rivers, magnetization of type-II superconductors, and elastoplastic deformations. We outline the main steps of such models derivation and try to clarify the origin of this similarity. New dual variational formulations, ana...
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Pucci and Serrin [21] conjecture that certain space dimensions behave “critically” in a semilinear polyharmonic eigenvalue problem. Up to now only a considerably weakened version of this conjecture could be shown. We prove that exactly in these dimensions an embedding inequality for higher order Sobolev spaces on bounded domains with an optimal embedding constant may be improved by adding a “li...
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ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2007
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2006.10.007