1,721,005 research outputs found
Simplified Excision Techniques for Free Discontinuity Problems in Several Variables
No full textAbstractOne of the methods proposed for the study of the problems with a free discontinuity set in two variables has been considered here under slightly different abstract assumptions from those in the previous papers. The technical difficulties are in this new setting simplified and less background is required to the reader. Moreover, applications to problems in several variables can be found thanks to a Sobolev-type theorem which ensures the Hölder continuity of certain functions out of a suitable neighborhood of their discontinuity set. Many of the results established so far for the case of two dimensions can be so extended to the general case. A new property is also proved
Min-max levels on the double natural constraint
No full textA question about the possibility of using min-max methods on the double natural constraint, in spite of its lack of regularity, has been raised in some recent papers. In this note we give an answer by topological arguments which show the equivalence between constrained and unconstrained min-max classes, avoiding in this way any regularity problem
A note on compactness-type properties with respect to Lorentz norms of bounded subset of a Sobolev Space
No full text
Concentration analysis in Banach spaces
Full text linkThe concept of a profile decomposition formalizes concentration compactness arguments on the functional-analytic level, providing a powerful refinement of the Banach-Alaoglu weak-star compactness theorem. We prove existence of profile decompositions for general bounded sequences in uniformly convex Banach spaces equipped with a group of bijective isometries, thus generalizing analogous results previously obtained for Sobolev spaces and for Hilbert spaces. Profile decompositions in uniformly convex Banach spaces are based on the notion of Delta-convergence by Lim [Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60 (1976) 179-182] instead of weak convergence, and the two modes coincide if and only if the norm satisfies the well-known Opial condition, in particular, in Hilbert spaces and l(p)-spaces, but not in L-p(R-N), p not equal 2 Delta-convergence appears naturally in the context of fixed point theory for non-expansive maps. The paper also studies the connection of Delta-convergence with the Brezis-Lieb lemma and gives a version of the latter without an assumption of convergence a.
Synchronic and asynchronic descriptions of irrigation problems.
No full textIn this paper we complete our work started in [31], where the present paper was announced;
in order to set a unified theory of the irrigation problem. The main result of the paper is the
equivalence of the various formulations introduced so far as well as a new one introduced
here. To this aim we introduce several geometric and analytical concepts which are essential
for reaching our final goal even if they may deserve an intrinsic interest in themselves
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