Non-Homogeneous Boundary Value Problems and Applications: Volume III
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1973
|
| Series: | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete
183 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 1. Our essential objective is the study of the linear, non-homogeneous problems: (1) Pu = I in CD, an open set in RN, (2) fQjtl = gj on am (boundary of m), lor on a subset of the bound m"J am 1 < f < v, where P is a linear differential operator in m and where the Q/s are linear differential operators on am. In Volumes 1 and 2, we studied, for particular classes of systems {P, Qj}, problem (1), (2) in classes of Sobolev spaces (in general constructed starting from P) of positive integer or (by interpolation) non-integer order; then, by transposition, in classes of Sobolev spaces of negative order, until, by passage to the limit on the order, we reached the spaces of distributions of finite order. In this volume, we study the analogous problems in spaces of infinitely differentiable or analytic functions or of Gevrey-type functions and by duality, in spaces of distributions, of analytic functionals or of Gevrey type ultra-distributions. In this manner, we obtain a clear vision (at least we hope so) of the various possible formulations of the boundary value problems (1), (2) for the systems {P, Qj} considered here |
| Physical Description: | 1 Online-Ressource (XII, 310 p) |
| ISBN: | 9783642653933 9783642653957 |
| DOI: | 10.1007/978-3-642-65393-3 |
Staff View
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| id | DE-604.BV042422873 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T06:38:45Z |
| institution | BVB |
| isbn | 9783642653933 9783642653957 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858290 |
| oclc_num | 863794610 |
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| physical | 1 Online-Ressource (XII, 310 p) |
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| publishDate | 1973 |
| publishDateSearch | 1973 |
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| publisher | Springer Berlin Heidelberg |
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| series | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| series2 | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| spelling | Lions, Jacques-Louis 1928-2001 Verfasser (DE-588)124055397 aut Non-Homogeneous Boundary Value Problems and Applications Volume III by J. L. Lions, E. Magenes Berlin, Heidelberg Springer Berlin Heidelberg 1973 1 Online-Ressource (XII, 310 p) txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 183 1. Our essential objective is the study of the linear, non-homogeneous problems: (1) Pu = I in CD, an open set in RN, (2) fQjtl = gj on am (boundary of m), lor on a subset of the bound m"J am 1 < f < v, where P is a linear differential operator in m and where the Q/s are linear differential operators on am. In Volumes 1 and 2, we studied, for particular classes of systems {P, Qj}, problem (1), (2) in classes of Sobolev spaces (in general constructed starting from P) of positive integer or (by interpolation) non-integer order; then, by transposition, in classes of Sobolev spaces of negative order, until, by passage to the limit on the order, we reached the spaces of distributions of finite order. In this volume, we study the analogous problems in spaces of infinitely differentiable or analytic functions or of Gevrey-type functions and by duality, in spaces of distributions, of analytic functionals or of Gevrey type ultra-distributions. In this manner, we obtain a clear vision (at least we hope so) of the various possible formulations of the boundary value problems (1), (2) for the systems {P, Qj} considered here Mathematics Mathematics, general Mathematik Magenes, Enrico 1923-2010 Sonstige (DE-588)1089130783 oth Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 183 (DE-604)BV049758308 183 https://doi.org/10.1007/978-3-642-65393-3 Verlag Volltext |
| spellingShingle | Lions, Jacques-Louis 1928-2001 Non-Homogeneous Boundary Value Problems and Applications Volume III Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete Mathematics Mathematics, general Mathematik |
| title | Non-Homogeneous Boundary Value Problems and Applications Volume III |
| title_auth | Non-Homogeneous Boundary Value Problems and Applications Volume III |
| title_exact_search | Non-Homogeneous Boundary Value Problems and Applications Volume III |
| title_full | Non-Homogeneous Boundary Value Problems and Applications Volume III by J. L. Lions, E. Magenes |
| title_fullStr | Non-Homogeneous Boundary Value Problems and Applications Volume III by J. L. Lions, E. Magenes |
| title_full_unstemmed | Non-Homogeneous Boundary Value Problems and Applications Volume III by J. L. Lions, E. Magenes |
| title_short | Non-Homogeneous Boundary Value Problems and Applications |
| title_sort | non homogeneous boundary value problems and applications volume iii |
| title_sub | Volume III |
| topic | Mathematics Mathematics, general Mathematik |
| topic_facet | Mathematics Mathematics, general Mathematik |
| url | https://doi.org/10.1007/978-3-642-65393-3 |
| volume_link | (DE-604)BV049758308 |
| work_keys_str_mv | AT lionsjacqueslouis nonhomogeneousboundaryvalueproblemsandapplicationsvolumeiii AT magenesenrico nonhomogeneousboundaryvalueproblemsandapplicationsvolumeiii |