共查询到20条相似文献,搜索用时 15 毫秒
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Wojciech S. Ożański 《Comptes Rendus Mathematique》2018,356(2):198-206
We extend the generalised comparison principle for the Monge–Ampère equation due to Rauch & Taylor (1977) [15] to nonconvex domains. From the generalised comparison principle, we deduce bounds (from above and below) on solutions to the Monge–Ampère equation with sign-changing right-hand side. As a consequence, if the right-hand side is nonpositive (and does not vanish almost everywhere), then the equation equipped with a constant boundary condition has no solutions. In particular, due to a connection between the two-dimensional Navier–Stokes equations and the Monge–Ampère equation, the pressure p in 2D Navier–Stokes equations on a bounded domain cannot satisfy in Ω unless (at any fixed time). As a result, at any time there exists such that . 相似文献
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We show that the intersection dimension of graphs with respect to several hereditary properties can be bounded as a function of the maximum degree. As an interesting special case, we show that the circular dimension of a graph with maximum degree Δ is at most . We also obtain bounds in terms of treewidth. 相似文献
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Lorenzo Brasco Giovanni Franzina Berardo Ruffini 《Journal of Functional Analysis》2018,274(6):1825-1863
We consider the Schrödinger operator for negative potentials V, on open sets with positive first eigenvalue of the Dirichlet–Laplacian. We show that the spectrum of is positive, provided that V is greater than a negative multiple of the logarithmic gradient of the solution to the Lane–Emden equation (for some ). In this case, the ground state energy of is greater than the first eigenvalue of the Dirichlet–Laplacian, up to an explicit multiplicative factor. This is achieved by means of suitable Hardy-type inequalities, that we prove in this paper. 相似文献
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