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Related papers: Boundary value problems for general first-order el…

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To empower the mathematical hitchhiker wishing to use operator methods in geometry and topology, we present this user's guide to first-order elliptic boundary value problems. Existence, regularity, and Fredholmness are discussed for general…

Analysis of PDEs · Mathematics 2025-10-21 Christian Baer , Lashi Bandara

We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the…

Differential Geometry · Mathematics 2019-07-25 Christian Baer , Werner Ballmann

We consider first-order elliptic differential operators acting on vector bundles over smooth manifolds with smooth boundary, which is permitted to be noncompact. Under very mild assumptions, we obtain a regularity theory for sections in the…

Differential Geometry · Mathematics 2026-02-12 Christian Baer , Lashi Bandara

This paper investigates realisations of elliptic differential operators of general order on manifolds with boundary following the approach of B\"ar-Ballmann to first order elliptic operators. The space of possible boundary values of…

Analysis of PDEs · Mathematics 2023-04-21 Lashi Bandara , Magnus Goffeng , Hemanth Saratchandran

We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we…

Analysis of PDEs · Mathematics 2007-05-23 Thomas Krainer

Free bondary value problem for elliptic differential-operator equations with variable coefficients is studied. The uniform maximal regularity properties and Fredholmness of this problem are obtained in vector-valued Holder spaces.

Analysis of PDEs · Mathematics 2017-06-06 Veli Shakhmurov

We define a class of boundary value problems on manifolds with fibered boundary. This class is in a certain sense a deformation between the classical boundary value problems and the Atiyah-Patodi-Singer problems in subspaces. The boundary…

Operator Algebras · Mathematics 2007-05-23 A. Yu. Savin , B. Yu. Sternin

We prove regularity for a class of boundary value problems for first order elliptic systems, with boundary conditions determined by spectral decompositions, under coefficient differentiability conditions weaker than previously known. We…

Differential Geometry · Mathematics 2007-05-23 P. T. Chrusciel , R. Bartnik

We develop an elliptic theory based in $L^2$ of boundary value problems for general wedge differential operators of first order under only mild assumptions on the boundary spectrum. In particular, we do not require the indicial roots to be…

Analysis of PDEs · Mathematics 2013-10-29 Thomas Krainer , Gerardo A. Mendoza

We investigate elliptic boundary-value problems for which the maximum of the orders of the boundary operators is equal to or greater than the order of the elliptic differential equation. We prove that the operator corresponding to an…

Analysis of PDEs · Mathematics 2020-07-28 Tetiana Kasirenko , Aleksandr Murach

We study linear boundary-value problems for systems of first-order ordinary differential equations with the most general boundary conditions in the normed spaces of continuously differentiable functions on a finite closed interval. The…

Classical Analysis and ODEs · Mathematics 2026-01-05 Vitalii Soldatov

We investigate an arbitrary regular elliptic boundary-value problem given in a bounded Euclidean domain with infinitely smooth boundary. We prove that the operator of the problem is bounded and Fredholm in appropriate pairs of H\"ormander…

Analysis of PDEs · Mathematics 2015-09-15 Anna V. Anop , Aleksandr A. Murach

We give necessary and sufficient conditions for the solvability of some semilinear elliptic boundary value problems involving the Laplace operator with linear and nonlinear highest order boundary conditions involving the Laplace-Beltrami…

Analysis of PDEs · Mathematics 2013-11-14 Ciprian G. Gal , Gisele Ruiz Goldstein , Jerome A. Goldstein , Silvia Romanelli , Mahamadi Warma

We present an introduction to boundary value problems for Dirac-type operators on complete Riemannian manifolds with compact boundary. We introduce a very general class of boundary conditions which contains local elliptic boundary…

Differential Geometry · Mathematics 2024-10-02 Christian Baer , Werner Ballmann

We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.

Complex Variables · Mathematics 2022-05-03 Dariush Ehsani

In a refined Sobolev scale, we investigate an elliptic boundary-value problem with additional unknown functions in boundary conditions for which the maximum of orders of boundary operators is grater than or equal to the order of the…

Analysis of PDEs · Mathematics 2018-04-03 Tetiana Kasirenko , Iryna Chepurukhina

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…

Analysis of PDEs · Mathematics 2020-04-29 B. -W. Schulze , J. Seiler

This note is a description of some of the results obtained by the authors in connection with the problem in the title. These, discussed following a summary of background material concerning wedge differential operators, consist of the…

Analysis of PDEs · Mathematics 2014-03-28 Thomas Krainer , Gerardo A. Mendoza

A regular elliptic boundary-value problem over a bounded domain with a smooth boundary is studied. We prove that the operator of this problem is a Fredholm one in the two-sided refined scale of the functional Hilbert spaces and generates a…

Analysis of PDEs · Mathematics 2009-03-30 Vladimir A. Mikhailets , Aleksandr A. Murach

This paper considers boundary value problems for a class of singular elliptic operators which appear naturally in the study of asymptotically anti-de Sitter (aAdS) spacetimes. These problems involve a singular Bessel operator acting in the…

Analysis of PDEs · Mathematics 2018-08-14 Oran Gannot
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