Holomorphic extension of fundamental solutions of elliptic linear partial differential operators of higher order with analytic coefficients

DOI10.1016/j.bulsci.2014.09.004zbMath1417.35024OpenAlexW1982779086MaRDI QIDQ1756322

Serge Lukasiewicz

Publication date: 14 January 2019

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2014.09.004

zbMATH Keywords

singularitiesholomorphic extensionfundamental solutionelliptic PDENilsson class

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Integral representations of solutions to PDEs (35C15) Continuation of analytic objects in several complex variables (32D15) Analyticity in context of PDEs (35A20) Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels) (32A26) Higher-order elliptic equations (35J30)

Cites Work

• Singularités des systèmes différentiels de Gauss-Manin. Avec des contributions de Lo Kam Chan, Philippe Maisonobe et Jean-Etienne Rombaldi
• Holomorphic extension of fundamental solutions of elliptic linear partial differential operators of the second order with analytic coefficients
• On holonomic systems of microdifferential equations. III: Systems with regular singularities
• Some growth and ramification properties of certain integrals on algebraic manifolds
• Lacunas for hyperbolic differential operators with constant coefficients.I
• Le théorème de l'indice relatif
• Uniformisation de la solution du problème linéaire analytique de Cauchy près de la variété qui porte les données de Cauchy. (Problème de Cauchy. I)
• Intégrales de Nilsson et faisceaux constructibles
• Un prolongement de la transformation de Laplace qui transforme la solution unitaire d'un opérateur hyperbolique en sa solution élémentaire. (Problème de Cauchy. IV.)
• Le calcul différentiel et intégral sur une variété analytique complexe. (Problème de Cauchy. III.)
• Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients
• La solution unitaire d'un opérateur différentiel linéaire. (Problème de Cauchy. II.)
• The Functional Transformations Required by the Theory of Partial Differential Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Holomorphic extension of fundamental solutions of elliptic linear partial differential operators of higher order with analytic coefficients