Trace Formulas for a Conformable Fractional Diffusion Operator

Inverse Nodal Problem for a Conformable Fractional Diffusion Operator

In this paper, a diffusion operator including conformable fractional derivatives of order α (α in (0,1)) is considered. The asymptotics of the eigenvalues, eigenfunctions and nodal points of the operator are obtained. Furthermore, an effective procedure for solving the inverse nodal problem is given.

Inverse problems for a conformable fractional Sturm-Liouville operator

In this paper, a Sturm-Liouville boundary value problem equiped with conformable fractional derivates is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra and classical spectral data. We also study on half-inverse problem and prove a Hochstadt and Lieberman-type theorem.

Trace Hardy--Sobolev--Mazy'a inequalities for the half fractional Laplacian

In this work we establish trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for weakly mean convex domains. We accomplish this by obtaining a new weighted Hardy type estimate which is of independent inerest. We then produce Hardy-Sobolev-Maz'ya inequalities for the spectral half Laplacian. This covers a critical case left open in \cite{FMT1}.

Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian

In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use them to produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants for various fractional Laplacians. In the case where the domain is the half space our results cover the full range of the exponent $s \in (0,1)$ of the fractional Laplacians. We answer in particular an open problem raised by Frank and Seiringer \cite{FS}.

m-耗散广义阻抗边界条件、离散谱与分数阶Sobolev空间之间的逐点乘子

M-dissipative generalized impedance boundary conditions, discrete spectra, and pointwise multipliers between fractional Sobolev spaces

本文研究了有界Lipschitz域中m-耗散广义阻抗边界条件下声学算子的性质，证明了其紧预解算子与阻抗算子紧性等价，并应用于谱离散性及波动方程。