共查询到20条相似文献,搜索用时 46 毫秒
1.
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
2.
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
3.
Xuan Thinh Duong Irina Holmes Ji Li Brett D. Wick Dongyong Yang 《Journal of Functional Analysis》2019,276(4):1007-1060
In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian on the upper half space and the reflection Neumann Laplacian on with respect to the weights associated to and respectively. This in turn yields a weak factorization for the corresponding weighted Hardy spaces, where in particular, the weighted class associated to is strictly larger than the Muckenhoupt weighted class and contains non-doubling weights. In our study, we also make contributions to the classical Muckenhoupt–Wheeden weighted Hardy space (BMO space respectively) by showing that it can be characterized via the area function (Carleson measure respectively) involving the semigroup generated by the Laplacian on and that the duality of these weighted Hardy and BMO spaces holds for Muckenhoupt weights with while the previously known related results cover only . We also point out that this two weight commutator theorem might not be true in the setting of general operators L, and in particular we show that it is not true when L is the Dirichlet Laplacian on . 相似文献
4.
We prove a sharp estimate for the k-modulus of smoothness, modelled upon a -Lebesgue space, of a function f in , where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, , and . This sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into generalized Hölder spaces defined by means of the k-modulus of smoothness. General results are illustrated with examples. In particular, we obtain a generalization of the classical Jawerth embeddings. 相似文献
5.
In this paper, we study semilinear elliptic systems with critical nonlinearity of the form
(0.1)
for , Q has quadratic growth in ?u. Our work is motivated by elliptic systems for harmonic map and biharmonic map. When , such a system does not have smooth regularity in general for weak solutions, by a well-known example of J. Frehse. Classical results of harmonic map, proved by F. Hélein (for ) and F. Béthuel (for ), assert that a weak solution of harmonic map is always smooth. We extend Béthuel's result to general system (0.1), that a weak solution of the system is smooth for . For a fourth order semilinear elliptic system with critical nonlinearity which extends biharmonic map, we prove a similar result, that a weak solution of such system is always smooth, for . We also construct various examples, and these examples show that our regularity results are optimal in various sense. 相似文献
6.
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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8.
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
9.
We study ground states of two-component Bose–Einstein condensates (BEC) with trapping potentials in , where the intraspecies interaction and the interspecies interaction ?β are both attractive, , , and β are all positive. The existence and non-existence of ground states are classified completely by investigating equivalently the associated -critical constraint variational problem. The uniqueness and symmetry-breaking of ground states are also analyzed under different types of trapping potentials as , where () is fixed and w is the unique positive solution of in . The semi-trivial limit behavior of ground states is tackled in the companion paper [12]. 相似文献
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11.
Ryosuke Hyakuna 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(4):1081-1104
This paper is concerned with the Cauchy problem for the Hartree equation on with the nonlinearity of type . It is shown that a global solution with some twisted persistence property exists for data in the space under some suitable conditions on γ and spatial dimension . It is also shown that the global solution u has a smoothing effect in terms of spatial integrability in the sense that the map is well defined and continuous from to , which is well known for the solution to the corresponding linear Schrödinger equation. Local and global well-posedness results for hat -spaces are also presented. The local and global results are proved by combining arguments by Carles–Mouzaoui with a new functional framework introduced by Zhou. Furthermore, it is also shown that the global results can be improved via generalized dispersive estimates in the case of one space dimension. 相似文献
12.
Michael Giudici S.P. Glasby Cai Heng Li Gabriel Verret 《Journal of Pure and Applied Algebra》2019,223(3):1217-1226
Let Γ be a finite G-vertex-transitive digraph. The in-local action of is the permutation group induced by a vertex-stabiliser on the set of in-neighbours of the corresponding vertex. The out-local action is defined analogously. Note that and may not be isomorphic. We thus consider the problem of determining which pairs are possible. We prove some general results, but pay special attention to the case when and are both quasiprimitive. (Recall that a permutation group is quasiprimitive if each of its nontrivial normal subgroups is transitive.) Along the way, we prove a structural result about pairs of finite quasiprimitive groups of the same degree, one being (abstractly) isomorphic to a proper quotient of the other. 相似文献
13.
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
14.
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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16.
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
17.
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
18.
We are concerned with magneto-micropolar fluid equations (1.3)–(1.4). The global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the magneto-micropolar-Navier–Stokes (MMNS) system, we obtain global existence and large time behavior of solutions near a constant states in . Appealing to a refined pure energy method, we first obtain a global existence theorem by assuming that the norm of the initial data is small, but the higher order derivatives can be arbitrary large. If the initial data belongs to homogeneous Sobolev norms or homogeneous Besov norms , we obtain the optimal decay rates of the solutions and its higher order derivatives. As an immediate byproduct, we also obtain the usual type of the decay rates without requiring that the norm of initial data is small. At last, we derive a weak solution to (1.3)–(1.4) in with large initial data. 相似文献
19.
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
20.
With appropriate hypotheses on the nonlinearity f, we prove the existence of a ground state solution u for the problem where , V is a bounded continuous potential and F the primitive of f. We also show results about the regularity of any solution of this problem. 相似文献