Related papers: Well-posedness, regularity and asymptotic analyses…

This is the first part of a series of two papers where we study perturbations of divergence form second order elliptic operators $-\mathop{\operatorname{div}} A \nabla$ by first and zero order terms, whose coefficients lie in critical…

This paper deals with a nonlocal model for a hyperbolic phase field system coupling the standard energy balance equation for temperature with a dynamic for the phase variable: the latter includes an inertial term and a nonlocal…

This paper is devoted to studying non-commensurate fractional order planar systems. Our contributions are to derive sufficient conditions for the global attractivity of non-trivial solutions to fractional-order inhomogeneous linear planar…

We study the well-posedness of a linear control system $\Sigma(A,B,C,D)$ with unbounded control and observation operators. To this end we associate to our system an operator matrix $\mathcal{A}$ on a product space $\mathcal{X}^p$ and call…

This paper is dedicated to the study of the semilinear fractional diffusion-wave equation. We provide estimates on the families of linear operators related to the problem in the fractional power scale associated with the Laplace operator.…

In the paper, we derive an existence result for a nonlinear nonautonomous partial elliptic system on an open bounded domain with Dirichlet boundary conditions, containg fractional powers of the weak Dirichlet-Laplace operator that are meant…

In this paper we discuss the existence and regularity of solutions of strongly indefinite systems involving fractional elliptic operators on a smooth bounded domain $\Omega$ in $\R^n$.

The paper arXiv:1804.11290 contains well-posedness and regularity results for a system of evolutionary operator equations having the structure of a Cahn-Hilliard system. The operators appearing in the system equations were fractional…

We study the spectral behavior of higher order elliptic operators upon domain perturbation. We prove general spectral stability results for Dirichlet, Neumann and intermediate boundary conditions. Moreover, we consider the case of the…

We develop a phase-space framework for fractional generalised anharmonic oscillators and their heat semigroups on weighted modulation spaces. We consider operators of the form \[ \mathcal{H}_{k,l}=(-\Delta)^{l}+V(x), \] where $V$ is a…

We present an analytical investigation of the asymptotic behavior of non-resonance eigenvalues for the fractional Schr\"odinger operator under homogeneous Neumann boundary conditions. Our findings reveal an intriguing convergence: as the…

In this paper, we consider a new class of multi phase operators with variable exponents, which reflects the inhomogeneous characteristics of hardness changes when multiple different materials are combined together. We at first deal with the…

Let $\,T^{j,k}_{N}:L^{p}(B)\, \rightarrow\,L^{q}([0,1])\,$ be the oscillatory integral operators defined by $\;\displaystyle T^{j,k}_{N}f(s):=\int_{B} \,f(x)\,e^{\imath N{|x|}^{j}s^{k}}\,dx, \quad (j,k)\in\{1,2\}^{2},\,$ where $\,B\,$ is…

In this paper we present a general extrapolated elliptic regularity result for second order differential operators in divergence form on fractional Sobolev-type spaces of negative order $X^{s-1,q}_D(\Omega)$ for $s > 0$ small, including…

Boundedness properties of operators associated with non-degenerate symmetric $\alpha$-stable, $\alpha \in (1,2)$, probability measures on $\mathbb{R}^d$ are investigated on appropriate, Euclidean or otherwise, $L^p$-spaces, $p \in…

In this paper we discuss the existence, uniqueness and regularity of solutions of the following system of coupled semilinear Poisson equations on a smooth bounded domain $\Omega$ in $\mathbb{R}^n$: \[ \left\{{llll} \mathcal{A}^s u= v^p &…

In this work we consider the asymptotic behavior of the nonlinear semigroup defined by a semilinear parabolic problem with homogeneous Neumann boundary conditions posed in a bounded region of the plane that degenerates into a line segment…

This work is about global H\"older regularity for solutions to elliptic partial differential equations subject to mixed boundary conditions on irregular domains. There are two main results. In the first, we show that if the domain of the…

A nonlinear extension of the Caginalp phase field system is considered that takes thermal memory into account. The resulting model, which is a first-order approximation of a thermodynamically consistent system, is inspired by the theories…

We consider nonlinear diffusive evolution equations posed on bounded space domains, governed by fractional Laplace-type operators, and involving porous medium type nonlinearities. We establish existence and uniqueness results in a suitable…