排序方式: 共有87条查询结果,搜索用时 38 毫秒
1.
Alessandro Morando Paola Trebeschi Tao Wang 《Journal of Differential Equations》2019,266(9):5397-5430
We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme. 相似文献
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We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation. 相似文献
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In the first part of this paper we give suitable spectral properties of the adjoint operators induced by appropriate perturbations of some hyperbolic linear vector fields. These properties are useful to prove general facts based on the Nash–Moser inverse function theorem. In the second part of this work we study circumstances where a global linearization of a vector field X in a real numerical space is feasible and where some diffeomorphisms which are close to exp(X) can be embedded in a flow. 相似文献
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By exploiting a suitable Trudinger–Moser inequality for fractional Sobolev spaces, we obtain existence and multiplicity of solutions for a class of one-dimensional nonlocal equations with fractional diffusion and nonlinearity at exponential growth. 相似文献
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张文丽 《应用泛函分析学报》2014,(4):346-350
研究了—(p,q)-Laplacian拟线性椭圆方程组.当连续函数V和W在两种情形下,利用Moser迭代技巧和Ljusternik-Schnirelmann畴数理论,建立了方程组正解的存在性和多重性结果. 相似文献
6.
Lin Feng Wang Ze Yu Zhang Liang Zhao Yu Jie Zhou 《Mathematical Methods in the Applied Sciences》2017,40(4):992-1002
We prove that on a smooth metric measure space with m ?Bakry–Émery curvature bounded from below by ?(m ? 1)K for some constant K ≥0 (i.e., Ricf ,m ≥?(m ? 1)K ), the following degenerate elliptic equation (0.1) has no nonconstant positive solution when p > 1 and constant λ f ,p satisfies Our approach is based on the local Sobolev inequality and the Moser's iterative technique and is different from Cheng‐Yau's method, which was used by Wang‐Zhu in 2012 to derive a same Liouville theorem when 1 < p ≤2, Ricf ,m ≥?(m ? 1)K and the sectional curvature is bounded from below. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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紧致流形上Laplacian的第一特征值的下界估计一直以来是人们非常感兴趣的问题之一.本文在整体曲率Pinching较小的条件之下考虑这个问题,得到了相应几何条件之下的Laplacian第一特征值的一个下界估计. 相似文献
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In a previous work (Adimurthi and Yang, 2010 [2]), Adimurthi–Yang proved a singular Trudinger–Moser inequality in the entire Euclidean space . Precisely, if and , then there holds for any , where and is the area of the unit sphere in . The above inequality is sharp in the sense that if , all integrals are still finite but the supremum is infinity. In this paper, we concern extremal functions for these singular inequalities. The regular case has been considered by Li and Ruf (2008) [12] and Ishiwata (2011) [11]. We shall investigate the singular case and prove that for all , and , extremal functions for the above inequalities exist. The proof is based on blow-up analysis. 相似文献
10.
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