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961.
黄启亮 《数学的实践与认识》2013,43(7)
引入独立参数及共轭指数,应用权函数方法和实分析技巧,建立一个零齐次核的带最佳常数的Hilbert型积分不等式,并考虑其等价形式及其逆式. 相似文献
962.
In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities. 相似文献
963.
Energies for the first four singlet and triplet S states of a helium atom confined at the center of an impenetrable sphere are reported. All calculations used explicitly correlated Hylleraas basis sets. The first triplet state is shown to lie below the first excited singlet state only when the confinement radius is greater than 0.988a0. A simple configuration interaction calculation was performed in parallel with Hylleraas calculation. The one-electron atomic orbitals of the configuration treatment provide insight into the physical concepts behind the numerical results of the Hylleraas treatment. This was particularly helpful in understanding the level crossing and avoided crossings observed with changing confinement radius. 相似文献
964.
965.
A. Boulkhemair 《偏微分方程通讯》2013,38(9):1439-1447
We give a proof of the Poincaré inequality in W 1, p (Ω) with a constant that is independent of Ω ? , where is a set of uniformly bounded and uniformly Lipschitz domains in ? n . As a byproduct, we obtain the following: The first non vanishing eigenvalues λ2(Ω) of the standard Neumann (variational) boundary value problem on Ω for the Laplace operator are bounded below by a positive constant if the domains Ω vary and remain uniformly bounded and uniformly Lipschitz regular. 相似文献
966.
We consider the Schrödinger equation on a compact manifold, in the presence of a nonlinear damping term, which is homogeneous and sublinear. For initial data in the energy space, we construct a weak solution, defined for all positive time, which is shown to be unique. In the one-dimensional case, we show that it becomes zero in finite time. In the two and three-dimensional cases, we prove the same result under the assumption of extra regularity on the initial datum. 相似文献
967.
Upper bounds are obtained for the heat content of an open set D in a geodesically complete Riemannian manifold M with Dirichlet boundary condition on ?D, and non-negative initial condition. We show that these upper bounds are close to being sharp if (i) the Dirichlet-Laplace-Beltrami operator acting in L 2(D) satisfies a strong Hardy inequality with weight δ2, (ii) the initial temperature distribution, and the specific heat of D are given by δ?α and δ?β respectively, where δ is the distance to ?D, and 1 < α <2, 1 < β <2. 相似文献
968.
Matthieu Felsinger 《偏微分方程通讯》2013,38(9):1539-1573
Weak solutions to parabolic integro-differential operators of order α ∈ (α0, 2) are studied. Local a priori estimates of Hölder norms and a weak Harnack inequality are proved. These results are robust with respect to α↗2. In this sense, the presentation is an extension of Moser's result from [20]. 相似文献
969.
We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove that the solutions are in general not unique. The case where the zero order term has the opposite sign was already intensively studied and the uniqueness is the rule. 相似文献
970.
Sami Mustapha 《偏微分方程通讯》2013,38(1-2):245-275
Abstract We study the regularity of the free boundary in the two membranes problem. We prove that around any point the free boundary is either a C 1, α surface or a cusp, as in the obstacle problem. We also prove C 1, 1 regularity for the pair of functions solving the problem. 相似文献