A duality theorem for solutions of elliptic equations
Let L be a second order linear partial differential operator of elliptic type on a domain Ω of ℝm with coefficients in C∞(Ω). We consider the linear space of all solutions of the equation Lu=0 on Ω with the topology of uniform convergence on compact subsets and describe the topological dual of this...
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| Format: | Article |
| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171290000114 |
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| _version_ | 1832547407411281920 |
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| author | Pierre Blanchet |
| author_facet | Pierre Blanchet |
| author_sort | Pierre Blanchet |
| collection | DOAJ |
| description | Let L be a second order linear partial differential operator of elliptic type on a domain Ω of ℝm with coefficients in C∞(Ω). We consider the linear space of all solutions of the equation Lu=0 on Ω with the topology of uniform convergence on compact subsets and describe the topological dual of this space. It turns out that this dual may be identified with the space of solutions of an adjoint equation near the boundary modulo the solutions of this adjoint equation on the entire domain. |
| format | Article |
| id | doaj-art-0c6d12cb8f0f4c80a024e4125aa14071 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0c6d12cb8f0f4c80a024e4125aa140712025-02-03T06:44:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-01131738510.1155/S0161171290000114A duality theorem for solutions of elliptic equationsPierre Blanchet0Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USALet L be a second order linear partial differential operator of elliptic type on a domain Ω of ℝm with coefficients in C∞(Ω). We consider the linear space of all solutions of the equation Lu=0 on Ω with the topology of uniform convergence on compact subsets and describe the topological dual of this space. It turns out that this dual may be identified with the space of solutions of an adjoint equation near the boundary modulo the solutions of this adjoint equation on the entire domain.http://dx.doi.org/10.1155/S0161171290000114partial differential equationsellipticityduality. |
| spellingShingle | Pierre Blanchet A duality theorem for solutions of elliptic equations International Journal of Mathematics and Mathematical Sciences partial differential equations ellipticity duality. |
| title | A duality theorem for solutions of elliptic equations |
| title_full | A duality theorem for solutions of elliptic equations |
| title_fullStr | A duality theorem for solutions of elliptic equations |
| title_full_unstemmed | A duality theorem for solutions of elliptic equations |
| title_short | A duality theorem for solutions of elliptic equations |
| title_sort | duality theorem for solutions of elliptic equations |
| topic | partial differential equations ellipticity duality. |
| url | http://dx.doi.org/10.1155/S0161171290000114 |
| work_keys_str_mv | AT pierreblanchet adualitytheoremforsolutionsofellipticequations AT pierreblanchet dualitytheoremforsolutionsofellipticequations |