162,211 research outputs found
``Bubble-tower'' radial solutions in the slightly supercritical Brezis-Nirenberg problem
No full textAbstractIn this paper, we consider the Brezis–Nirenberg problem in dimension N⩾4, in the supercritical case. We prove that if the exponent gets close to N+2N−2 and if, simultaneously, the bifurcation parameter tends to zero at the appropriate rate, then there are radial solutions which behave like a superposition of bubbles, namely solutions of the formγ∑j=1k11+Mj4N−2|y|2(N−2)/2Mj(1+o(1)),γ=(N(N−2))(N−2)/4,where Mj→+∞ and Mj=o(Mj+1) for all j. These solutions lie close to turning points “to the right” of the associated bifurcation diagram
Fast diffusion equations: Matching large time asymptotics by relative entropy methods
No full textA non self-similar change of coordinates provides improved matching asymptotics of the solutions of the fast diffusion equation for large times, compared to already known results, in the range for which Barenblatt solutions have a finite second moment. The method is based on relative entropy estimates and a time-dependent change of variables which is determined by second moments, and not by the scaling corre- sponding to the self-similar Barenblatt solutions, as it is usually done.The research that led to the present paper was partially supported by a grant of the group GNFM of INdAM
Dolbeault and J-Invariant Cohomologies on Almost Complex Manifolds
No full textIn this paper we relate the cohomology of J-invariant forms to the Dolbeault cohomology of an almost complex manifold. We find necessary and sufficient condition for the inclusion of the former into the latter to be true up to isomorphism. We also extend some results obtained by J. Cirici and S. O. Wilson about the computation of the left-invariant cohomology of nilmanifolds to the setting of solvmanifolds. Several examples are given
Dolbeault and -invariant cohomologies on almost complex manifolds
No full textIn this paper we relate the cohomology of -invariant forms to the
Dolbeault cohomology of an almost complex manifold. We find necessary and
sufficient condition for the inclusion of the former into the latter to be true
up to isomorphism. We also extend some results obtained by J. Cirici and S.O.
Wilson about the computation of the left-invariant cohomology of nilmanifolds
to the setting of solvmanifolds. Several examples are given
A phase planeanalysis of the ``Multi-bubbling'' phenomenon in some slightlysupercritical equations
No full textThe purpose of this paper is to present some recent results in two slightly super-critical problems known as the Brezis-Nirenberg problem in dimension nge3 and an equation involving the exponential nonlinearity in dimension nge2. For that purpose, we perform a phase plane analysis which emphasizes the common heuristic properties of the two problems, although more precise estimates can be obtained in some cases by variational methods.ou
Szegö Mappings, Harmonic Forms, and Dolbeault Cohomology
No full textAbstractLet G/L be the quotient of a semisimple Lie Group G by the centralizer L of a torus. The author constructs an explicit intertwinig operator from derived functor modules, realized in the Langlands classification, into Dolbeault cohomology on G/L. This operator produces strongly harmonic forms. This paper generalizes the results in (L. Barchini, A. W. Knapp, and R. Zierau, J. Funct. Anal.107 (1992), 302-341) by dropping the condition real rank L = real rand G
Almost complex structures, transverse complex structures, and transverse Dolbeault cohomology
No full textInternational audienceWe define a transverse Dolbeault cohomology associated to any almost complex structure j on a smooth manifold M . This we do by extending the notion of transverse complex structure and by introducing a natural j-stable involutive limit distribution with such a transverse complex structure. We relate this transverse Dolbeault cohomology to the generalized Dolbeault cohomology of (M, j) introduced by Cirici and Wilson in [3], showing that the (p, 0) cohomology spaces coincide. This study of transversality leads us to suggest a notion of minimally non-integrable almost complex structure
Duality in the suband super critical bubbling in the Brezis-Nirenberg problem fordimension
No full text"Multi-bubbling" in some slightly supercritical equations: the case of the exponentialnonlinearity.
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