Details

Autor(en) / Beteiligte

• Lions, J. L
• Magenes, E

Titel

Non-Homogeneous Boundary Value Problems and Applications : Volume III [Elektronische Ressource]

Ist Teil von

• Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete : 183

Ort / Verlag

Berlin, Heidelberg : Springer Berlin Heidelberg

Erscheinungsjahr

1973

Link zum Volltext

• Volltext

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• 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 boundm"J am 1 < f < v, where Pis 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 c1asses of systems {P, Qj}, problem (1), (2) in c1asses of Sobolev spaces (in general constructed starting from P) of positive integer or (by interpolation) non-integer order; then, by transposition, in c1asses 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 inlinitely dilferentiable or analytic Itlnctions or of Gevrey-type I~mctions and by duality, in spaces 01 distribtltions, of analytic Itlnctionals or of Gevreytype ultra-distributions. In this manner, we obtain a c1ear 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