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981.
The paper deals with the large solutions of the problems
$\triangle u=u^p$ and $\triangle u= e^u.$ They blow up at the boundary. It is well-known that the first term in their asymptotic behaviour near the boundary is independent of the geometry of the boundary. We determine the second term which depends on the mean curvature of the nearest point on the boundary. The computation is based on suitable upper and lower solutions and on estimates given in [4]. In the last section these estimates are used together with the P-function to establish the asymptotic behaviour of the gradients. 相似文献
982.
We determine the Lie superalgebras that are graded by the
root system B(m,n) of the
orthosymplectic Lie superalgebra osp(2m +
1,2n).
Mathematics Subject Classification (2000) Primary 17B70, Secondary 17A70 相似文献
983.
The authors prove that a proper monomial holomorphic mapping from the two-ball to the N-ball has degree at most 2N-3, and
that this result is sharp. The authors first show that certain group-invariant polynomials (related to Lucas polynomials)
achieve the bound. To establish the bound the authors introduce a graph-theoretic approach that requires determining the number
of sinks in a directed graph associated with the quotient polynomial. The proof also relies on a result of the first author
that expresses all proper polynomial holomorphic mappings between balls in terms of tensor products. 相似文献
984.
Let R(t)=P(t)/Q(t) be a quotient of real polynomials. We show that ∫exp(iR(t)) dt/t has a uniform bound with a bound depending only on the degrees of P and Q and not on their coefficients. Also
LP estimates are obtained for certain associated singular integral operators. 相似文献
985.
Moxun Tang 《Journal of Differential Equations》2003,189(1):148-160
We prove uniqueness of positive radial solutions to the semilinear elliptic equation , subject to the Dirichlet boundary condition on an annulus in . As a by-product, our argument also provides a much simpler, if not the simplest, new proof for the uniqueness of positive solutions to the same problem in a finite ball or in the whole space . 相似文献
986.
Michael Winkler 《Journal of Differential Equations》2003,192(2):445-474
We study nonglobal positive solutions to the Dirichlet problem for ut=up(Δu+u) in bounded domains, where 0<p<2. It is proved that the set of points at which u blows up has positive measure and the blow-up rate is exactly . If either the space dimension is one or p<1, the ω-limit set of consists of continuous functions solving . In one space dimension it is shown that actually as t→T, where w coincides with an element of a one-parameter family of functions inside each component of its positivity set; furthermore, we study the size of the components of {w>0} with the result that this size is uniquely determined by Ω in the case p<1, while for p>1, the positivity set can have the maximum possible size for certain initial data, but it may also be arbitrarily close to the minimal length π. 相似文献
987.
Julián López-Gómez 《Journal of Differential Equations》2003,195(1):25-45
In this paper we ascertain the blow-up rate of the large solutions of a class of sublinear elliptic boundary value problems with a weight function in front of the nonlinearity that vanishes on the boundary of the underlying domain, Ω, at different rates according to the point of the boundary, . All previous results in the literature assumed the decay rate of the underlying weight function to be the same at any point of ∂Ω. This hypothesis substantially simplified the mathematical analysis of the problem, as it allowed constructing global sub and supersolutions in an open neighborhood of ∂Ω. Obtaining general results requires localizing at each particular point of the boundary, making particularly involved the mathematical analysis of the problem. 相似文献
988.
The context of much of the work in this paper is that of a backward-shift invariant subspace of the form , where B is some infinite Blaschke product. We address (but do not fully answer) the question: For which B can one find a (convergent) sequence in KB such that the sequence of real measures converges weak-star to some nontrivial singular measure on ? We show that, in order for this to hold, KB must contain functions with nontrivial singular inner factors. And in a rather special setting, we show that this is also sufficient. Much of the paper is devoted to finding conditions (on B) that guarantee that KB has no functions with nontrivial singular inner factors. Our primary result in this direction is based on the “geometry” of the zero set of B. 相似文献
989.
Kehe Zhu 《Journal of Functional Analysis》2003,202(2):327-341
For a finite Blaschke product B let TB denote the analytic multiplication operator (also called a Toeplitz operator) on the Bergman space of the unit disk. We show that the defect operators and both map the Bergman space to the Hardy space and the Hardy space to the Dirichlet space. 相似文献
990.
Marian-Ioan Munteanu 《Journal of Geometry》2003,77(1-2):140-151
Let (M, ) be a contact manifold. Consider a particular class of gauge transformations for the contact
form . In this note we study the harmonicity of the identity map of the manifold M, of dimension three, endowed
with the Webster metric g and with another metric $\widetilde{g}$ obtained from g after a gauge transformation. 相似文献