共查询到20条相似文献,搜索用时 10 毫秒
1.
It was once conjectured that if A is a uniform algebra on its maximal ideal space X, and if each point of X is a peak point for A, then A = C(X). This peak point conjecture was disproved by Brian Cole in 1968. However, Anderson and Izzo showed that the peak point conjecture
does hold for uniform algebras generated by smooth functions on smooth two-manifolds with boundary. The corresponding assertion
for smooth three-manifolds is false, but Anderson, Izzo, and Wermer established a peak point theorem for polynomial approximation
on real-analytic three-manifolds with boundary. Here we establish a more general peak point theorem for real-analytic three-manifolds
with boundary analogous to the two-dimensional result. We also show that if A is a counterexample to the peak point conjecture generated by smooth functions on a manifold of arbitrary dimension, then
the essential set for A has empty interior. 相似文献
2.
Consider a second order divergence form elliptic operator L with complex bounded measurable coefficients. In general, operators based on L, such as the Riesz transform or square function, may lie beyond the scope of the Calderón–Zygmund theory. They need not be
bounded in the classical Hardy, BMO and even some L
p
spaces. In this work we develop a theory of Hardy and BMO spaces associated to L, which includes, in particular, a molecular decomposition, maximal and square function characterizations, duality of Hardy
and BMO spaces, and a John–Nirenberg inequality.
S. Hofmann was supported by the National Science Foundation. 相似文献
3.
N. M. Ivochkina 《Journal of Fixed Point Theory and Applications》2008,4(1):47-56
We adapt to degenerate m-Hessian evolution equations the notion of m-approximate solutions introduced by N. Trudinger for m-Hessian elliptic equations, and we present close to necessary and sufficient conditions guaranteeing the existence and uniqueness
of such solutions for the first initial boundary value problem.
Dedicated to Professor Felix Browder 相似文献
4.
5.
Combining elements of the b-calculus and the theory of elliptic boundary value problems, we solve the gluing problem for b-determinants
of Dirac type operators on manifolds with cylindrical ends. As a corollary of our proof, we derive a gluing formula for the
b-eta invariant and also a relative invariant formula relating the b-spectral invariants on a manifold with cylindrical end
to the spectral invariants with the augmented APS boundary condition on the corresponding compact manifold with boundary. 相似文献
6.
Anna Maria Micheletti Angela Pistoia 《Calculus of Variations and Partial Differential Equations》2009,34(2):233-265
Given (M, g) a smooth compact Riemannian N-manifold, N ≥ 2, we show that positive solutions to the problem
are generated by stable critical points of the scalar curvature of g, provided is small enough. Here p > 2 if N = 2 and if N ≥ 3.
The authors are supported by Mi.U.R. project “Metodi variazionali e topologici nello studio di fenomeni non lineari”. 相似文献
7.
Our first basic model is the fully nonlinear dual porous medium equation with source
for which we consider the Cauchy problem with given nonnegative bounded initial data u0. For the semilinear case m=1, the critical exponent
was obtained by H. Fujita in 1966. For p ∈(1, p0] any nontrivial solution blows up in finite time, while for p > p0 there exist sufficiently small global solutions. During last thirty years such critical exponents were detected for many
semilinear and quasilinear parabolic, hyperbolic and elliptic PDEs and inequalities. Most of efforts were devoted to equations
with differential operators in divergent form, where classical techniques associated with weak solutions and integration by
parts with a variety of test functions can be applied. Using this fully nonlinear equation, we propose and develop new approaches
to calculating critical Fujita exponents in different functional settings.
The second models with a “semi-divergent” diffusion operator is the thin film equation with source
for which the critical exponent is shown to be
相似文献
8.
Given (M, g) a smooth compact Riemannian N-manifold, we prove that for any fixed positive integer K the problem
has a K-peaks solution, whose peaks collapse, as ε goes to zero, to an isolated local minimum point of the scalar curvature. Here p > 2 if N = 2 and .
E. N. Dancer was partially supported by the ARC. A. M. Micheletti and A. Pistoia are supported by Mi.U.R. Project “Metodi
variazionali e topologici nello studio di fenomeni non lineari”. 相似文献
9.
Nicolas Saintier 《Calculus of Variations and Partial Differential Equations》2009,35(3):385-407
We describe the asymptotic behaviour in Sobolev spaces of sequences of solutions of Paneitz-type equations [Eq. (E
α
) below] on a compact Riemannian manifold (M, g) which are invariant by a subgroup of the group of isometries of (M, g). We also prove pointwise estimates. 相似文献
10.
José Ignacio Royo Prieto Martintxo Saralegi-Aranguren Robert Wolak 《manuscripta mathematica》2008,126(2):177-200
For a riemannian foliation on a closed manifold M, it is known that is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form
(relatively to a suitable riemannian metric μ) is zero (cf. álvarez in Ann Global Anal Geom 10:179–194, 1992). In the transversally
orientable case, tautness is equivalent to the non-vanishing of the top basic cohomology group , where (cf. Masa in Comment Math Helv 67:17–27, 1992). By the Poincaré Duality (cf. Kamber et and Tondeur in Astérisque 18:458–471,
1984) this last condition is equivalent to the non-vanishing of the basic twisted cohomology group , when M is oriented. When M is not compact, the tautness class is not even defined in general. In this work, we recover the previous study and results
for a particular case of riemannian foliations on non compact manifolds: the regular part of a singular riemannian foliation
on a compact manifold (CERF).
J. I. Royo Prieto was partially supported by EHU06/05, by a PostGrant from the Basque Government and by the MCyT of the Spanish
Government. R. Wolak was partially supported by the KBN grant 2PO3A 021 25. 相似文献
11.
Feng-Yu Wang 《manuscripta mathematica》2009,128(3):343-358
By estimating the intrinsic distance and using known heat kernel upper bounds, the global Nash inequality with exact dimension is established for a class of square fields with algebraic growth induced by vector fields satisfying the Hörmander condition. As an application, a sufficient condition is presented for the log-Sobolev inequality to hold. Typical examples for Gruschin type operators and generalized Kohn-Lapacians on Heisenberg groups are provided. 相似文献
12.
In this paper we establish the multiplicity of positive solutions to second-order superlinear repulsive singular Neumann boundary
value problems. It is proved that such a problem has at least two positive solutions under reasonable conditions. Our nonlinearity
may be repulsive singular in its dependent variable and superlinear at infinity. The proof relies on a nonlinear alternative
of Leray-Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones.
相似文献
13.
James Kennedy 《Journal of Evolution Equations》2008,8(3):557-582
We give an extension of the Faber-Krahn inequality to the Laplacian Δ on bounded Lipschitz domains , with generalised Wentzell boundary conditions on ∂Ω, where β, γ are nonzero real constants. We prove that when β, γ > 0, the ball B minimises the first eigenvalue with respect to all Lipschitz domains Ω of the same volume as B, and that B is the unique minimiser amongst C
2-domains. We also consider β, γ not both positive, and slightly extend what is known about the associated Wentzell operator and its resolvent in addition
to considering an analogue of the Faber-Krahn inequality. This is based on the recent extension of the Faber-Krahn inequality
to the Robin Laplacian. We also give a version of Cheeger’s inequality for the Wentzell Laplacian when β, γ > 0.
相似文献
14.
Konrad Gröger Lutz Recke 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(3):263-285
This paper concerns boundary value problems for quasilinear second order elliptic systems which are, for example, of the type
Here Ω is a Lipschitz domain in
νj are the components of the unit outward normal vector field on ∂Ω, the sets Γβ are open in ∂Ω and their relative boundaries are Lipschitz hypersurfaces in ∂Ω. The coefficient functions are supposed to
be bounded and measurable with respect to the space variable and smooth with respect to the unknown vector function u and to the control parameter λ. It is shown that, under natural conditions, such boundary value problems generate smooth
Fredholm maps between appropriate Sobolev-Campanato spaces, that the weak solutions are H?lder continuous up to the boundary
and that the Implicit Function Theorem and the Newton Iteration Procedure are applicable. 相似文献
15.
Domenico Mucci 《manuscripta mathematica》2009,128(4):421-441
We deal with strong density results of smooth maps between two manifolds and in the fractional spaces given by the traces of Sobolev maps in W
1,p
. 相似文献
16.
In this paper we describe and analyze some modified boundary element methods to solve the exterior Dirichlet boundary value
problem for the Helmholtz equation. As in classical combined field integral equations also the proposed approach avoids spurious
modes. Moreover, the stability of related modified boundary element methods can be shown even in the case of Lipschitz boundaries.
The proposed regularization is done based on boundary integral operators which are already included in standard boundary element
formulations. Numerical examples are given to compare the proposed approach with other already existing regularized formulations. 相似文献
17.
Pierre Jammes 《manuscripta mathematica》2007,123(1):15-23
Let M
n
be an n-dimensional compact manifold, with n ≥ 3. For any conformal class C of riemannian metrics on M, we set , where μ
p,k
(M,g) is the kth eigenvalue of the Hodge laplacian acting on coexact p-forms. We prove that . We also prove that if g is a smooth metric such that , and n = 0,2,3 mod 4, then there is a non-zero corresponding eigenform of degree with constant length. As a corollary, on a four-manifold with non vanishing Euler characteristic, there is no such smooth
extremal metric. 相似文献
18.
An operatorX:
is said to be a generalized Toeplitz operator with respect to given contractionsT
1 andT
2 ifX=T
2XT1
*. The purpose of this line of research, started by Douglas, Sz.-Nagy and Foia, and Pták and Vrbová, is to study which properties of classical Toeplitz operators depend on their characteristic relation. Following this spirit, we give appropriate extensions of a number of results about Toeplitz operators. Namely, Wintner's theorem of invertibility of analytic Toeplitz operators, Widom and Devinatz's invertibility criteria for Toeplitz operators with unitary symbols, Hartman and Wintner's theorem about Toeplitz operator having a Fredholm symbol, Hartman and Wintner's estimate of the norm of a compactly perturbed Toeplitz operator, and the non-existence of compact classical Toeplitz operators due to Brown and Halmos.Dedicated to our friend Cora Sadosky on the occasion of her sixtieth birthday 相似文献
19.
We consider quite general h-pseudodifferential operators on R
n
with small random perturbations and show that in the limit h → 0 the eigenvalues are distributed according to a Weyl law with a probabality that tends to 1. The first author has previously
obtained a similar result in dimension 1. Our class of perturbations is different. 相似文献
20.
We investigate in detail the mapping properties of the maximal operator associated with the heat-diffusion semigroup corresponding
to expansions with respect to multi-dimensional standard Laguerre functions . Our interest is focused on the situation when at least one coordinate of the type multi-index α is smaller than 0. For such parameters α the Laguerre semigroup does not satisfy the general theory of semigroups, and the behavior of the associated maximal operator
on L
p
spaces is found to depend strongly on both α and the dimension.
A. Nowak was supported in part by MNiSW Grant N201 054 32/4285. 相似文献