相关论文: Anisotropic Calder\'{o}n Problem for a Non-Local S…

We study the inverse problem of recovering a tree graph together with the weights on its edges (equivalently a metric tree) from the knowledge of the Dirichlet-to-Neumann matrix associated with the Laplacian. We prove an explicit formula…

This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted Sobolev classes. We establish…

We investigate the electrochemical processes within an electrolyser cell, which are modelled by a coupled system of second-order quasi-linear elliptic PDEs. In this context, we study an inverse problem aiming to reconstruct both the…

We study Hermitian metrics with constant second scalar curvature on compact manifolds. We first consider a Yamabe-type problem for the second Bismut scalar curvature under a natural topological condition, and then analyze elliptic equations…

We consider the inverse problem of determining coefficients appearing in semilinear elliptic equations stated on Riemannian manifolds with boundary given the knowledge of the associated Dirichlet-to-Neumann map. We begin with a negative…

In this paper we prove a local Carleman estimate for second order elliptic equations with a general anisotropic Lipschitz coefficients having a jump at an interface. Our approach does not rely on the techniques of microlocal analysis. We…

In this paper we introduce and study a new Kelvin-type transform in the anisotropic setting. In particular, we deal with semilinear and quasilinear anisotropic elliptic problems in the entire space.

Let $M$ be an $m (\ge2)$-dimensional closed orientable submanifold in an $n$-dimensional complete simply-connected Riemannian manifold $N$, where the sectional curvature of $N$ is bounded above by $\delta$. When $\delta<0$, inspired by…

Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of…

We investigate elliptic operators with a symmetry that forces their index to vanish. We study the secondary index, defined modulo 2. We examine Callias-type operators with this symmetry on non-compact manifolds and establish mod 2 versions…

In this paper, we investigate the existence of weak solution for a Kirchhoff type problem driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions {\small$$…

We consider Calderon's inverse problem with partial data in dimensions $n \geq 3$. If the inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction, we show that this problem reduces to the invertibility…

We investigate properties of pseudodifferential operators on $L^2$ space on manifold with ends including asymptotically conical or hyperbolic ends. Our pseudodifferential operators are a generalization of the canonical quantization which…

We extend the results of a work by L. H\"ormander in 1990 concerning the resolution of the characteristic Cauchy problem for second order wave equations with regular first order potentials. The geometrical background of this work was a…

Non-local boundary conditions, such as the Atiyah-Patodi-Singer (APS) conditions, for Dirac operators on Riemannian manifolds are well understood while not much is known for such operators on spacetimes with timelike boundary. We define a…

This paper deals with the Cauchy problem associated to the nonlinear fourth-order Schr\"odinger equation with isotropic and anisotropic mixed dispersion. This model is given by the equation $i\partial _{t}u+\epsilon \Delta u+\delta A…

In this paper we consider an inverse problem of determining a minimal surface embedded in a Riemannian manifold. We show under a topological condition that if $\Sigma$ is a $2$-dimensional embedded minimal surface, then the knowledge of the…

A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…

We study the Cauchy problem involving non-local Ornstein-Uhlenbeck operators in finite and infinite dimensions. We prove classical solvability without requiring that the L\'evy measure corresponding to the large jumps part has a first…

In $L_2 (\mathbb{R}^d; \mathbb{C}^n)$, we consider a selfadjoint matrix strongly elliptic second order differential operator $\mathcal{A}_\varepsilon$ with periodic coefficients depending on $\mathbf{x}/\varepsilon$. We find approximations…