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The Weyl law of transmission eigenvalues and the completeness of generalized transmission eigenfunctions

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (8)

The transmission problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. After four ......

The Weyl formula for planar annuli

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (4)

We study the zeros of cross-product of Bessel functions and obtain their approximations, based on which we reduce the eigenvalue counting problem for ......

Anew formula for the L-p norm

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (4)

Recently, Brezis, Van Schaftingen and the second author [4] established a new formula for the. W-1,W-p norm of a function in C-c(infinity) (R-N). The ......

L-p-estimate of Schrodinger maximal function inhigher dimensions

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (5)

Almost everywhere convergence on the solution of Schrodinger equation is an important problem raised by Carleson in harmonic analysis. In recent years......

A study on a class of generalized Schrodinger operators

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (9)

In this paper, we consider the pointwise convergence for a class of generalized Schrodinger operators with suitable perturbations, and convergence rat......

Long time behavior and field-induced instabilities of smectic liquid crystals

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (3)

In this paper, we study long time behavior and dynamical instabilities of smectic liquid crystals in an applied magnetic field. Under a planar ansatz ......

Scaling limit of a directed polymer among a Poisson field of independent walks

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (5)

We consider a directed polymer model in dimension 1 + 1, where the disorder is given by the occupation field of a Poisson system of independent random......

Reconstruction in the Calderon problem on conformally transversally anisotropic manifolds

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (9)

We show that a continuous potential q can be constructively determined from the knowledge of the Dirichlet-to-Neumann map for the Schrodinger operator......

Eigenvalue estimates via weighted L-2-technique

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (2)

Under various elliptic boundary conditions, we obtain lower eigenvalue estimates for Dirac operators by using the weighted L-2-technique which has its......

Heat kernel upper bounds for symmetric Markov semigroups

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (4)

It is well known that Nash-type inequalities for symmetric Dirichlet forms are equivalent to on-diagonal heat kernel upper bounds for the associated s......

Monotonicity of positive solutions for nonlocal problems in unbounded domains

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (9)

In this paper, we consider the following problem {(-Delta)(p)(s)u(x) = f(u), u(x) > 0 in Omega, u(x) = 0 on R-n\Omega, where (-Delta)(p)(s) is the ......

On stable and finite Morse index solutions of the fractional Toda system

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 280 (4)

We develop a monotonicity formula for solutions of the fractional Toda system (-Delta)(s) f(alpha) = e(-(f alpha+1 - f alpha)) - e(-(f alpha - f alpha......

An application of atomic decomposition in Bergman spaces to the study of differences of composition operators (vol 262, pg 3872, 2021)

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (9)

In this note, the proof of the main result in the paper "An application of atomic decomposition in Bergman spaces to the study of difference of compos......

Rigidity theorems of spacelike entire self-shrinking graphs in the pseudo-Euclidean space

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (9)

In this paper, we firstly establish a new volume growth estimate for spacelike entire graphs in the pseudo-Euclidean space R-n(m+n). Then by using thi......

Two bipolynomial Roth theorems in R

期刊: JOURNAL OF FUNCTIONAL ANALYSIS, 2021; 281 (2)

We give two Roth theorems, related to the nonlinear configuration x, x + P-1(t), x + P-2(t) involving two polynomials, for sets in R of positive densi......

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