oai-hal-tel-00712008v4
type: Dataset
description: The aim of this work is the study of complete elliptic differential equations of second order with operator coefficients in a Banach space X. A concrete application of these equations is detailed, it concerns a transmission problem of electric potential in a biological cell where the membrane is considered as a thin layer. The originality of this work is the fact that unbounded operators which are considered do not commute necessarily. A new noncommutativity hypothesis is then introduced. The analysis is performed in two distinct functional frameworks: the Hölder spaces and the Lp spaces (X being a UMD space). First, the equation is studied on the whole real line and secondly in a bounded interval with Dirichlet boundary conditions. Existence, uniqueness and maximal regularity of the classical solution are proved under some conditions on the data in interpolation spaces. The techniques used are based on semigroup theory, Dunford functional calculus and interpolation theory. All the results are applied to concrete partial differential equations of elliptic or quasi-elliptic type.
issued: 2026-06-03T20:54:16.614475
language: fr
modified: 2026-06-03T20:54:16.614484
title: Unified study of partial differential equations of elliptic type governed by differential equations with operator coefficients in a noncommutative framework: concrete applications in Hölder and Lp spaces
contact point: Organization
  fn: CCSD
keyword: analytic-semigroup
keyword: biological-cell
keyword: boundary-condition
keyword: cadre-non-commutatif
keyword: calcul-fonctionnel-de-dunford
keyword: cellule-biologique
keyword: condition-aux-limites
keyword: couche-mince
keyword: dunford-functional-calculus
keyword: equation-differentielle-operationnelle-du-second-ordre-de-type-elliptique
keyword: espace-dinterpolation
keyword: espace-umd
keyword: infoeu-reposemanticsdoctoralthesis
keyword: interpolation-space
keyword: mathmath-apmathematics-mathanalysis-of-pdes-mathap
keyword: maximal-regularity
keyword: noncommutative-framework
keyword: probleme-de-transmission
keyword: regularite-maximale
keyword: second-order-operational-elliptic-differential-equation
keyword: semi-groupe-analytique
keyword: theses
keyword: thin-layer
keyword: transmission-problem
keyword: umd-space
landing page: https://theses.hal.science/tel-00712008

https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-tel-00712008v4/resource/2db3c8e9-3f9f-4c69-9601-b8fcd19d8fcd
type: Distribution
format: HTML
issued: 2026-06-03T20:54:16.637659
modified: 2026-06-03T20:54:16.506576
title: Unified study of partial differential equations of elliptic type governed by differential equations with operator coefficients in a noncommutative framework: concrete applications in Hölder and Lp spaces
access URL: https://theses.hal.science/tel-00712008

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type: Agent