A Cauchy problem for the Cauchy–Riemann operator

Autor:	Ibrahim Ly
Rok vydání:	2020
Předmět:	Cauchy problem Physics Pure mathematics Differential equation General Mathematics Weak solution Institut für Mathematik Boundary (topology) Cauchy–Riemann equations symbols.namesake Elliptic curve symbols Initial value problem Boundary value problem ddc:510
Zdroj:	Afrika Matematika. 32:69-76
ISSN:	2190-7668 1012-9405
DOI:	10.1007/s13370-020-00810-4
Popis:	We study the Cauchy problem for a nonlinear elliptic equation with data on a piece $${\mathcal {S}}$$ of the boundary surface $$\partial {\mathcal {X}}$$ . By the Cauchy problem is meant any boundary value problem for an unknown function u in a domain $${\mathcal {X}}$$ with the property that the data on $${\mathcal {S}}$$ , if combined with the differential equations in $${\mathcal {X}}$$ , allows one to determine all derivatives of u on $${\mathcal {S}}$$ by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near $${\mathcal {S}}$$ is guaranteed by the Cauchy–Kovalevskaya theorem. We discuss a variational setting of the Cauchy problem which always possesses a generalized solution.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::17ffc98a6d6e8c8d1a5cbdd5732e4beb https://doi.org/10.1007/s13370-020-00810-4 Zobrazit plný text záznamu Full text from SpringerLink