共查询到20条相似文献,搜索用时 31 毫秒
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We study the stress concentration, which is the gradient of the solution, when two smooth inclusions are closely located in a possibly anisotropic medium , . The governing equation may be degenerate of p-Laplace type, with . We prove optimal estimates for the blow-up of the gradient of the solution as the distance between the inclusions tends to zero. 相似文献
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Zhouxin Li 《Journal of Differential Equations》2019,266(11):7264-7290
We prove the existence of positive solutions of the following singular quasilinear Schrödinger equations at critical growth via variational methods, where , , , , . It is interesting that we do not need to add a weight function to control . 相似文献
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Let () be a bounded domain and . Put with . In this paper, we provide various necessary and sufficient conditions for the existence of weak solutions to where , , τ and ν are measures on Ω and ?Ω respectively. We then establish existence results for the system where , , , τ and are measures on Ω, ν and are measures on ?Ω. We also deal with elliptic systems where the nonlinearities are more general. 相似文献
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Rafael López 《Journal of Differential Equations》2019,266(7):3927-3941
We consider a smooth solution of the singular minimal surface equation defined in a bounded strictly convex domain of with constant boundary condition. If , we prove the existence a unique critical point of u. We also derive some and estimates of u by using the theory of maximum principles of Payne and Philippin for a certain family of Φ-functions. Finally we deduce an existence theorem of the Dirichlet problem when . 相似文献
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We establish a relationship between an inverse optimization spectral problem for the N-dimensional Schrödinger equation and a solution of the nonlinear boundary value problem . Using this relationship, we find an exact solution for the inverse optimization spectral problem, investigate its stability and obtain new results on the existence and uniqueness of the solution for the nonlinear boundary value problem. 相似文献
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Joachim Toft 《Applied and Computational Harmonic Analysis》2019,46(1):154-176
We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator is a Schatten-q operator from to and r-nuclear operator from to when for suitable p, q and r in . 相似文献
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In this paper, we consider the following nonlinear elliptic equation involving the fractional Laplacian with critical exponent: where and , is periodic in with . Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in , including infinite lattices. On the other hand, to obtain positive solution with infinite bumps such that the bumps locate in lattices in , the restriction on is in some sense optimal, since we can show that for , no such solutions exist. 相似文献
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Teresa DAprile 《Journal of Differential Equations》2019,266(11):7379-7415
We are concerned with the existence of blowing-up solutions to the following boundary value problem where Ω is a smooth and bounded domain in such that , is a positive smooth function, N is a positive integer and is a small parameter. Here defines the Dirac measure with pole at 0. We find conditions on the function a and on the domain Ω under which there exists a solution blowing up at 0 and satisfying as . 相似文献
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Qingbo Huang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(7):1869-1902
We develop interior and regularity theories for -viscosity solutions to fully nonlinear elliptic equations , where T is approximately convex at infinity. Particularly, regularity theory holds if operator T is locally semiconvex near infinity and all eigenvalues of are at least as . regularity for some Isaacs equations is given. We also show that the set of fully nonlinear operators of regularity theory is dense in the space of fully nonlinear uniformly elliptic operators. 相似文献
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We consider the exterior Dirichlet problem for the heterogeneous Helmholtz equation, i.e. the equation where both A and n are functions of position. We prove new a priori bounds on the solution under conditions on A, n, and the domain that ensure nontrapping of rays; the novelty is that these bounds are explicit in k, A, n, and geometric parameters of the domain. We then show that these a priori bounds hold when A and n are and satisfy certain monotonicity conditions, and thereby obtain new results both about the well-posedness of such problems and about the resonances of acoustic transmission problems (i.e. A and n discontinuous) where the transmission interfaces are only assumed to be and star-shaped; the novelty of this latter result is that until recently the only known results about resonances of acoustic transmission problems were for convex interfaces with strictly positive curvature. 相似文献
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Alexander Iksanov Konrad Kolesko Matthias Meiners 《Stochastic Processes and their Applications》2019,129(11):4480-4499
Let be Biggins’ martingale associated with a supercritical branching random walk, and let be its almost sure limit. Under a natural condition for the offspring point process in the branching random walk, we show that if the law of belongs to the domain of normal attraction of an -stable distribution for some , then, as , there is weak convergence of the tail process , properly normalized, to a random scale multiple of a stationary autoregressive process of order one with -stable marginals. 相似文献
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In this paper, we study the existence and concentration behavior of minimizers for , here and where and are constants. By the Gagliardo–Nirenberg inequality, we get the sharp existence of global constraint minimizers of for when , and . For the case , we prove that the global constraint minimizers of behave like for some when c is large, where is, up to translations, the unique positive solution of in and , and . 相似文献
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We are concerned with the following singularly perturbed Gross–Pitaevskii equation describing Bose–Einstein condensation of trapped dipolar quantum gases: where ε is a small positive parameter, , ? denotes the convolution, and is the angle between the dipole axis determined by and the vector x. Under certain assumptions on , we construct a family of positive solutions which concentrates around the local minima of V as . Our main results extend the results in J. Byeon and L. Jeanjean (2007) [6], which dealt with singularly perturbed Schrödinger equations with a local nonlinearity, to the nonlocal Gross–Pitaevskii type equation. 相似文献
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We study the non-linear minimization problem on with , and : where presents a global minimum α at with . In order to describe the concentration of around , one needs to calibrate the behavior of with respect to s. The model case is In a previous paper dedicated to the same problem with , we showed that minimizers exist only in the range , which corresponds to a dominant non-linear term. On the contrary, the linear influence for prevented their existence. The goal of this present paper is to show that for , and , minimizers do exist. 相似文献
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Liang Zhao 《Journal of Differential Equations》2019,266(9):5615-5624
In this paper, let be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation where are real constants. 相似文献
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Verena Bögelein Frank Duzaar Leah Schätzler Christoph Scheven 《Journal of Differential Equations》2019,266(11):7709-7748
We establish that solutions to the Cauchy–Dirichlet problem for functionals of linear growth can be obtained as limits of solutions to flows with p-growth in the limit . The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth. 相似文献