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1.
We prove that solutions for ¯ get 1/M-derivatives more than the data in Lp-Sobolev spaces on a bounded convex domain of finite type M by means of the integral kernel method. Also we prove that the Bergman projection is invariant under the Lp-Sobolev spaces of fractional orders by different methods from McNeal-Stein's. By using these results, we can get Lp-Sobolev estimates of order 1/M for the canonical solution for ¯.
The author was supported by grant No. R01-2000-000-00001-0 from the Basic Research Program of the Korea Science&Engineering Foundation. 相似文献
2.
The boundary behavior of the Bergman kernel function of a kind of Reinhardt domain is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points (Z,(Z-)). Let Ω be the Reinhardt domainm(X) where αj>0,j=1,2,…,n,N=N1+N2+…+Nn,‖Zj‖ is the standard Euclidean norm in CNj,j=1,2,…,n; and let K(Z,(W-)) be the Bergman kernel function of Ω. Then there exist two positive constants m and M,and a function F such that mF(Z,(Z-))≤K(Z,(Z-))≤MF(Z,(Z-))holds for every Z∈Ω. Here (X) and r(Z)=‖Z‖α-1 is the defining function of Ω. The constants m and M depend only on α=(α1,…,αn) and N1,N2,…,Nn,not on Z. This result extends some previous known results. 相似文献
3.
Acta Mathematica Hungarica - Let $$\sigma =\{\sigma_i |i\in I\}$$ be some partition of the set of all primes $$\mathbb{P}$$ and G be a finite group. A group is said to be $$\sigma$$ -primary if it... 相似文献
4.
ROOS Guy 《中国科学A辑(英文版)》2006,(9)
We study the complete Kahler-Einstein metric of a Hartogs domainΩbuilt on an irreducible bounded symmetric domainΩ, using a power Nμof the generic norm ofΩ.The generating function of the Kahler-Einstein metric satisfies a complex Monge-Ampere equation with a boundary condition. The domainΩis in general not homogeneous, but it has a subgroup of automorphisms, the orbits of which are parameterized by X∈[0,1[. This allows us to reduce the Monge-Ampere equation to an ordinary differential equation with a limit condition. This equation can be explicitly solved for a special valueμ0 ofμ.. We work out the details for the two exceptional symmetric domains. The special valueμ0 seems also to be significant for the properties of other invariant metrics like the Bergman metric; a conjecture is stated, which is proved for the exceptional domains. 相似文献
5.
We study the complete K?hler-Einstein metric of a Hartogs domain
built on an irreducible bounded symmetric domain sW, using a power N
μ of the generic norm of Ω. The generating function of the K?hler-Einstein metric satisfies a complex Monge-Ampère equation
with a boundary condition. The domain
is in general not homogeneous, but it has a subgroup of automorphisms, the orbits of which are parameterized by X ε [0, 1[. This allows us to reduce the Monge-Ampère equation to an ordinary differential equation with a limit condition.
This equation can be explicitly solved for a special value μ0 of μ. We work out the details for the two exceptional symmetric domains. The special value μ0 seems also to be significant for the properties of other invariant metrics like the Bergman metric; a conjecture is stated,
which is proved for the exceptional domains. 相似文献
6.
7.
We point out an error in the paper (Monatsh Math. doi:10.1007/s00605-013-0492-3, 2013) by Kang, and give new brief proofs of the main results. 相似文献
8.
Improving the rate of convergence of ‘high order finite elements’ on polygons and domains with cusps
Summary. Let u and uV V be the solution and, respectively, the discrete solution of the non-homogeneous Dirichlet problem u=f on , u|=0. For any m and any bounded polygonal domain , we provide a construction of a new sequence of finite dimensional subspaces Vn such that where f Hm–1() is arbitrary and C is a constant that depends only on and not on n (we do not assume u Hm+1()). The existence of such a sequence of subspaces was first proved in a ground–breaking paper by Babuka [8]. Our method is different; it is based on the homogeneity properties of Sobolev spaces with weights and the well–posedness of non-homogeneous Dirichlet problem in suitable Sobolev spaces with weights, for which we provide a new proof, and which is a substitute of the usual shift theorems for boundary value problems in domains with smooth boundary. Our results extended right away to domains whose boundaries have conical points. We also indicate some of the changes necessary to deal with domains with cusps. Our numerical computation are in agreement with our theoretical results.The authors were supported in part by the NSF grant DMS 02-09497. Victor Nistor was also partially supported by NSF grant DMS 02-00808. 相似文献
9.
The time-harmonic Maxwell boundary value problem in polygonal domains of R2 is considered. The behaviour of the solution in the neighbourhood of nonregular boundary points is given and asymptotic error estimates in L2- and in curl-div-norm for a finite element approximation of the solution are derived 相似文献
10.
Bertram Kostant 《Transformation Groups》2010,15(4):909-919
A proof (by Serre and by Cohen, Griess and Lisser) verified, in the special case of E
8, a conjecture of mine, that the finite projective group L
2(61) embeds in
E8( \mathbbC ) {E_8}\left( \mathbb{C} \right) . Subsequently, Griess and Ryba have shown (using computers) that L
2(49) and, in addition, (established by Serre without computers) L
2(41) also embed in
E8( \mathbbC ) {E_8}\left( \mathbb{C} \right) . That is, if K = 30, 24, 20 and k ∈ K then L
2(2k + 1) embeds in
E8( \mathbbC ) {E_8}\left( \mathbb{C} \right) . In this paper we show that the “Borel” subgroup B(k) of L
2(2k + 1), k ∈ K, has a uniform construction. The theorem uses a result of T. Springer on the existence in
E8( \mathbbC ) {E_8}\left( \mathbb{C} \right) of three regular elements of the Weyl group, having orders k ∈ K, and associated to the regular, subregular and subsubregular nilpotent elements. Springer’s result generalizes (in the E
8 case) a 1959 general result of mine relating the principal nilpotent element with the Coxeter element. 相似文献
11.
The Hasse–Weil–Serre bound is improved for low genus curves over finite fields with discriminant from by studying maximal and minimal curves. 相似文献
12.
Maps are studied, i.e., cell decompositions of closed two-dimensional surfaces, or two-dimensional atoms which encode bifurcations of Liouville fibrations of non-degenerate integrable Hamiltonian systems. Any finite group G is proved to be a symmetry group of an orientable map (of an atom). Moreover, one such map X(G) is constructed algorithmically. Upper bounds are obtained for the minimal genus Mg(G) of an orientable map with the given symmetry group G and for the minimal number of vertices, edges, and sides of such maps. 相似文献
13.
Benson Dave Iyengar Srikanth B. Krause Henning Pevtsova Julia 《Mathematische Zeitschrift》2017,287(3-4):947-965
Mathematische Zeitschrift - We introduce the notion of $$\pi $$ -cosupport as a new tool for the stable module category of a finite group scheme. In the case of a finite group, we use this to give... 相似文献
14.
Let U be a multiply-connected fixed attracting Fatou domain of a rational map f.We prove that there exist a rational map g and a completely invariant Fatou domain V of g such that(f,U) and(g,V) are holomorphically conjugate,and each non-trivial Julia component of g is a quasi-circle which bounds an eventually superattracting Fatou domain of g containing at most one postcritical point of g.Moreover,g is unique up to a holomorphic conjugation. 相似文献
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16.
Given a pair of vector spacesV andW over a countable fieldF and a probability spaceX, one defines apolynomial measure preserving action ofV onX to be a compositionT o ϕ, where ϕ:V→W is a polynomial mapping andT is a measure preserving action ofW onX. We show that the known structure theory of measure preserving group actions extends to polynomial actions and establish
a Furstenberg-style multiple recurrence theorem for such actions. Among the combinatorial corollaries of this result are a
polynomial Szemerédi theorem for sets of positive density in finite rank modules over integral domains, as well as the following
fact:Let
be a finite family of polynomials with integer coefficients and zero constant term. For any α>0, there exists N ∈ ℕ such
that whenever F is a field with |F|≥N and E ⊆F with |E|/|F|≥α, there exist u∈F, u≠0, and w∈E such that w+ϕ(u)∈E for all ϕ∈
.
The first two authros are supported by NSF, grant DMS-0070566 and DMS-0245350. The second author was supported by the A. Sloan
Foundation. The third author is supported by NSF, grant DMS-0200700. 相似文献
17.
Z. Brzeźniak T. Caraballo J.A. Langa Y. Li G. Łukaszewicz J. Real 《Journal of Differential Equations》2013
We show that the stochastic flow generated by the 2-dimensional Stochastic Navier–Stokes equations with rough noise on a Poincaré-like domain has a unique random attractor. One of the technical problems associated with the rough noise is overcomed by the use of the corresponding Cameron–Martin (or reproducing kernel Hilbert) space. Our results complement the result by Brze?niak and Li (2006) [10] who showed that the corresponding flow is asymptotically compact and also generalize Caraballo et al. (2006) [12] who proved existence of a unique attractor for the time-dependent deterministic Navier–Stokes equations. 相似文献
18.
New characterizations of finite supersoluble groups 总被引:13,自引:0,他引:13
Let A be a subgroup of a group G and X a nonempty subset of G.A is called an X- semipermutable subgroup of G if A has a supplement T in G such that for every subgroup T_1 of T there exists an clement x∈X such that AT_i~x=T_i~xA.On the basis of this concept we obtain some new characterizations of finite supersoluble groups. 相似文献
19.
20.
Semigroup Forum - A semigroup S is called a $$\varDelta $$ -semigroup if the lattice of its congruences forms a chain relative to the inclusion. A local automorphism of a semigroup S is defined as... 相似文献