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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2014/656959 |
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| _version_ | 1832552169377628160 |
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| author | Mauricio Bravo Vera |
| author_facet | Mauricio Bravo Vera |
| author_sort | Mauricio Bravo Vera |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-910b8f43e7cc41038a425bf82f9a063b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-910b8f43e7cc41038a425bf82f9a063b2025-02-03T05:59:23ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252014-01-01201410.1155/2014/656959656959Nonlinear Equations of Infinite Order Defined by an Elliptic SymbolMauricio Bravo Vera0Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, ChileThe 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.http://dx.doi.org/10.1155/2014/656959 |
| spellingShingle | Mauricio Bravo Vera Nonlinear Equations of Infinite Order Defined by an Elliptic Symbol International Journal of Mathematics and Mathematical Sciences |
| title | Nonlinear Equations of Infinite Order Defined by an Elliptic Symbol |
| title_full | Nonlinear Equations of Infinite Order Defined by an Elliptic Symbol |
| title_fullStr | Nonlinear Equations of Infinite Order Defined by an Elliptic Symbol |
| title_full_unstemmed | Nonlinear Equations of Infinite Order Defined by an Elliptic Symbol |
| title_short | Nonlinear Equations of Infinite Order Defined by an Elliptic Symbol |
| title_sort | nonlinear equations of infinite order defined by an elliptic symbol |
| url | http://dx.doi.org/10.1155/2014/656959 |
| work_keys_str_mv | AT mauriciobravovera nonlinearequationsofinfiniteorderdefinedbyanellipticsymbol |