Related papers: Extension theory for elliptic partial differential…
We investigate the existence, uniqueness, and $L^1$-contractivity of weak solutions to a porous medium equation with fractional diffusion on an evolving hypersurface. To settle the existence, we reformulate the equation as a local problem…
We show that elliptic complexes of (pseudo)differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the…
The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which…
We study asymptotic behaviors of solutions to the Loewner-Nirenberg problem in domains with conic singularities and establish asymptotic expansions with respect to two normal directions simultaneously. The spherical domains over which cones…
We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also…
The focus of this study is on exploring some qualitative properties of solutions to a class of semilinear elliptic problems in bounded domains, where the boundary conditions depend non-locally on the unknown solution at specified interior…
In this paper we develop the global symbolic calculus of pseudo-differential operators generated by a boundary value problem for a given (not necessarily self-adjoint or elliptic) differential operator. For this, we also establish elements…
In this note self-adjoint extensions of symmetric operators are investigated by using the abstract technique of quasi boundary triples and their Weyl functions. The main result is an extension of Theorem 2.6 in [5] which provides sufficient…
In our previous paper [GSV2020], we proved that the complementary components of a ring domain in $\mathbb{R}^n$ with large enough modulus may be separated by an annular ring domain and applied this result to boundary correspondence problems…
We generalize Roe's index theorem for graded generalized Dirac operators on amenable manifolds to multigraded elliptic uniform pseudodifferential operators. The generalization will follow from a local index theorem that is valid on any…
We prove a semiclassical resolvent estimate for a broad class of non-self-adjoint, non-elliptic pseudodifferential operators in the low-lying spectral regime. The proof relies on improved ellipticity properties for the symbol of the…
For a class of non-selfadjoint semiclassical pseudodifferential operators with double characteristics, we study bounds for resolvents and estimates for low lying eigenvalues. Specifically, assuming that the quadratic approximations of the…
Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique solution for all…
We consider a class of pseudodifferential operators with a doubly characteristic point, where the quadratic part of the symbol fails to be elliptic but obeys an averaging assumption. Under suitable additional assumptions, semiclassical…
We extend in two directions the notion of perturbations of Carleson type for the Dirichlet problem associated to an elliptic real second-order divergence-form (possibly degenerate, not necessarily symmetric) elliptic operator. First, in…
We consider second order elliptic operators with real, nonsymmetric coefficient functions which are subject to mixed boundary conditions. The aim of this paper is to provide uniform resolvent estimates for the realizations of these…
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 $\R^n$.
We have studied possible applications of a particular pseudo-differential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The…
Based on the Fourier extension, we propose an oversampling collocation method for solving the elliptic partial differential equations with variable coefficients over arbitrary irregular domains. This method only uses the function values on…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…