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1.
The paper considers the asymptotic behaviour of the heat contentof a riemannian manifold M, when Dirichlet conditions are imposedon a small compact subset of M. 2000 Mathematics Subject Classification58J35, 35K05. 相似文献
2.
Given a first order elliptic partial differential equation weconstruct a solution which solves a given RiemannHilbertboundary value problem whose coefficients have singularitiesof the first kind at a finite number of some prescribed isolatedpoints and are Holdercontinuous outside those pointswhile the free term has a finite number of integrable powersingularities at some prescribed points. It is shown that thesolution belongs to some weighted Sobolev space W1,p(D;), wherethe weight function = (z;D) is the distance of the variablepoint z from the boundary D raised to a certain power. The problemis solved by first reducing it to an analogous problem for holomorphicfunctions. The latter is then solved. 2000 Mathematics SubjectClassification 35F15, 35F30, 35J55, 35J65, 36J67. 相似文献
3.
The presentation of the quantum cohomology of the moduli spaceof stable vector bundles of rank two and odd degree with fixeddeterminant over a Riemann surface of genus g > 2 is obtained.The argument avoids the use of gauge theory, providing an alternativeproof to that given by the author in Duke Math. J. 98 (1999)525540. 2000 Mathematics Subject Classification 14N35(primary); 14H60, 53D45 (secondary). 相似文献
4.
Assuming that the integrated density of states of a Schrödingeroperator admits a high-energy asymptotic expansion, the authorsgive explicit formulae for the coefficients of this expansionin terms of the heat invariants. 2000 Mathematics Subject Classification35J10, 47F05, 35P20. 相似文献
5.
Giorgio Davide Di; Lunardi Alessandra; Schnaubelt Roland 《Proceedings London Mathematical Society》2005,91(3):703-737
We study the operator Lu(t):= u'(t) A(t) u(t) on Lp(R; X) for sectorial operators A(t), with t R, on a Banachspace X that are asymptotically hyperbolic, satisfy the AcquistapaceTerreniconditions, and have the property of maximal Lp-regularity.We establish optimal regularity on the time interval R showingthat L is closed on its minimal domain. We further give conditionsfor ensuring that L is a semi-Fredholm operator. The Fredholmproperty is shown to persist under A(t)-bounded perturbations,provided they are compact or have small A(t)-bounds. We applyour results to parabolic systems and to generalized OrnsteinUhlenbeckoperators. 2000 Mathematics Subject Classification 35K20, 35K90,47A53. 相似文献
6.
Upper bounds are obtained for the heat content and the torsionalrigidity of a complete Riemannian manifold M, assuming a Hardyinequality for the Dirichlet Laplacian on M. 2000 MathematicsSubject Classification 35J05, 35K05, 58J35. 相似文献
7.
In this paper, the behaviour of the positive eigenfunction of in u| = 0, p > 1, isstudied near its critical points. Under some convexity and symmetryassumptions on , is seen to have a unique critical point atx = 0; also, the behaviour of both and is determined nearby.Positive solutions u to some general problems pu = f(u)in , u| = 0, are also considered, with some convexity restrictionson u. 2000 Mathematics Subject Classification 35B05 (primary),35J65, 35J70 (secondary). 相似文献
8.
On the Existence of Extremals for the Sobolev Trace Embedding Theorem with Critical Exponent 总被引:3,自引:0,他引:3
In this paper, the existence problem is studied for extremalsof the Sobolev trace inequality W1,p()Lp*(), where is a boundedsmooth domain in RN, p*=p(N1)/(Np), is the criticalSobolev exponent, and 1 < p < N. 2000 Mathematics SubjectClassification 35J65 (primary), 35B33 (secondary). 相似文献
9.
We consider the uniqueness of the positive solution to a semilinearelliptic equation with Dirichlet boundary condition and thenonlinearity satisfying f(0)<0 and having asymptotic sublineargrowth rate. A similar idea is also applied to the nonexistenceof a positive solution to a superlinear problem. 2000 MathematicsSubject Classification 35J65 (primary), 35B40 (secondary). 相似文献
10.
This paper considers the cone multiplier operator which is definedby
where and . For 3/2 < µ < 3/14, sharp Lp Lq estimatesand endpoint estimates for Sµ are obtained. 2000 MathematicsSubject Classification 42B15 (primary). 相似文献
11.
There exists a set U in the plane, such that elements of U correspondto minimal stable solutions of a two-parameter elliptic system.For points on the boundary of U, there exist weak solutionsto the elliptic system. The paper studies the properties ofthe curve . 2000 Mathematics Subject Classification 35J55, 35B05,35K50, 35K55. 相似文献
12.
Given a principal ideal domain R of characteristic zero, containing1/2, and a two-cone X of appropriate connectedness and dimension,we present sufficient algebraic conditions for the Hopf algebraFH(X; R) to be isomorphic with the universal enveloping algebraof an R-free graded Lie algebra; here, F stands for free part(that is, quotient by the R-torsion), H for homology, and forthe Moore loop space functor. 2000 Mathematics Subject Classification55P35, 55P62, 57T05, 17B70, 17B35. 相似文献
13.
It is proved here that if is an elliptic function and q is the maximal multiplicity ofall poles of f, then the Hausdorff dimension of the Julia setof f is greater than 2 q/(q + 1), and the Hausdorff dimensionof the set of points that escape to infinity is less than orequal to 2q/(q + 1). In particular, the area of this latterset is equal to 0. 2000 Mathematics Subject Classification 37F35(primary); 37F10, 30D30 (secondary). 相似文献
14.
Some Singularly Perturbed Problems on Annuli and a Counterexample to a Problem of Gidas, Ni and Nirenberg 总被引:1,自引:0,他引:1
1991 Mathematics Subject Classification 35B05, 35J60. 相似文献
15.
Regularity of the Fractional Maximal Function 总被引:2,自引:0,他引:2
The purpose of this work is to show that the fractional maximaloperator has somewhat unexpected regularity properties. Themain result shows that the fractional maximal operator mapsLp-spaces boundedly into certain first-order Sobolev spaces.It is also proved that the fractional maximal operator preservesfirst-order Sobolev spaces. This extends known results for theHardy-Littlewood maximal operator. 2000 Mathematics SubjectClassification 42B25, 46E35. 相似文献
16.
The integration-by-parts methods introduced in this paper improveupon the Lp estimates on transport densities given in the recentpaper by L. De Pascale and A. Pratelli (Calc. Var. Partial DifferentialEquations 14 (2002) 249274). 2000 Mathematics SubjectClassification 35Q99, 35B99. 相似文献
17.
We give a short proof of the fundamental result that the criticalprobability for bond percolation in the planar square latticeZ2 is equal to 1/2. The lower bound was proved by Harris, whoshowed in 1960 that percolation does not occur at p = 1/2. Theother, more difficult, bound was proved by Kesten, who showedin 1980 that percolation does occur for any p > 1/2. 2000Mathematics Subject Classification 60K35, 82B43. 相似文献
18.
This paper improves a theorem of Bergweiler on the zeros offunctions f g R with f meromorphic, g entire and Rrational. The proof yields a simple inequality for the numberof zeros and T(r, g). 2000 Mathematics Subject Classification30D35. 相似文献
19.
20.
Let C be a germ at O R2 of a real analytic plane curve, andCC its complexification; let Ct B be a fiber of a real smoothdeformation of C in the ball B = B(O,). The following inequalityis proved between the integrals of real curvature k of Ct andthose of Gaussian curvature K of :
The sharpness of this inequality is proved in the case whereC is a real irreducible germ. Similar results are proved foran affine algebraic curve C R2 of degree d. 2000 MathematicsSubject Classification 14H20, 14H50, 53A04. 相似文献