Nonlinear Equations of Infinite Order Defined by an Elliptic Symbol

The aim of this work is to show existence and regularity properties of equations of the form f(Δ)u=U(x,u(x)) on ℝn, in which f is a measurable function that satisfies some conditions of ellipticity and Δ stands for the Laplace operator on ℝn. Here, we define the class of functions to which f belongs...

Full description

Saved in:
Bibliographic Details
Published inInternational Journal of Mathematics and Mathematical Sciences Vol. 2014; no. 2014; pp. 1 - 7
Main Author Bravo Vera, Mauricio
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 2014
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
Hindawi Limited
Wiley
Subjects
Analysis
Deltas
Derivatives
Elliptic functions
Euclidean space
Functions (mathematics)
Hilbert space
Mathematical analysis
Nonlinear differential equations
Nonlinear equations
Operators
Regularity
Stands
Symbols
United States
Online AccessGet full text

Cover

More Information
Summary:The aim of this work is to show existence and regularity properties of equations of the form f(Δ)u=U(x,u(x)) on ℝn, in which f is a measurable function that satisfies some conditions of ellipticity and Δ stands for the Laplace operator on ℝn. Here, we define the class of functions to which f belongs and the Hilbert space in which we will find the solution to this equation. We also give the formal definition of f(Δ) explaining how to understand this operator.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0161-1712
1687-0425
DOI:10.1155/2014/656959