Related papers: Overdetermined fractional Serrin problem
We extend results of Caffarelli--Silvestre and Stinga--Torrea regarding a characterization of fractional powers of differential operators via an extension problem. Our results apply to generators of integrated families of operators, in…
Using Ursell operators for the study of the poperties of dilute degenerate gases
In this paper, we introduce a new multiple-parameters (multi-index) extension of the Wright function that arises from an eigenvalue problem for a case of hyper-Bessel operator involving Caputo fractional derivatives. We show that by giving…
In this paper we establish for the first time local semiconvexity estimates for fully nonlinear equations and for obstacle problems driven by integro-differential operators with general kernels. Our proof is based on the Bernstein…
New index transforms, involving the real part of the modified Bessel function of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue…
We obtain integral representations of the $n$-th derivatives of the Bessel functions with respect to the order. The numerical evaluation of these expressions is very efficient using a double exponential integration strategy. Also, from the…
An analogue of the Cauchy problem for the iterated multidimensional Klein- Gordon-Fock equation with a time-dependent Bessel operator is investigated. Applying the generalized Erdelyi-Kober operator of fractional order, the problem posed is…
In this paper, we solve a spectral problem about positive semi-definite trace-class pseudodifferential operators on modulation spaces which was posed by H. Feichtinger. Later, C. Heil and D. Larson rephrased the problem in the broader…
In this paper, we study a partially overdetermined mixed boundary value problem in a half ball. We prove that a domain in which this partially overdetermined problem admits a solution if and only if the domain is a spherical cap…
In this paper we study the subdifferential set of an operator. We give possible relation of the subdifferential set of an operator to that of its value, at a point where the operator attains its norm.
We derive a normal ordering formula for the operator \((xI)^n\), where \(I\) denotes the Volterra operator. The resulting coefficients are shown to coincide with the Bessel numbers. We also present two applications, along with a…
The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of Beta function recently defined by Shadab et al.[19]. Moreover, we establish some results related to the newly…
This thesis studies the extension problem for higher-order fractional powers of the heat operator $H=\Delta-\partial_t$ in $\mathbb{R}^{n+1}$. Specifically, given $s>0$ and indicating with $[s]$ its integral part, we study the following…
We introduce and study the properties of a new family of fractional differential and integral operators which are based directly on an iteration process and therefore satisfy a semigroup property. We also solve some ODEs in this new model…
A celebrated theorem of Serrin asserts that one overdetermined condition on the boundary is enough to obtain radial symmetry in the so-called one-phase overdetermined torsion problem. It is also known that imposing just one overdetermined…
We provide several characterizations of ring-shaped rotationally symmetric solutions to the Serrin problem in arbitrary dimensions.
In this note, we study a Serrin-type partially overdetermined problem proposed by Guo-Xia (Calc. Var. Partial Differential Equations 58: no. 160, 2019. https://doi.org/10.1007/s00526-019-1603-3, and prove a rigidity result that…
In this paper, we study the Babenko-Bechner-type inequality for the Fourier Weinstein transform associated with the Weinstein operator. We use this inequality to establish a new version of Young's type inequality.
We derive differential equations for multiplicative statistics of the Bessel determinantal point process depending on two parameters. In particular, we prove that such statistics are solutions to an integrable nonlinear partial differential…
Nowadays, fractional differential equations are a well established tool to model phenomena from the real world. Since the analytical solution is rarely available, there is a great effort in constructing efficient numerical methods for their…