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The boundary value problem for quasilinear degenerate and singular elliptic systems

โœ Scribed by Zu-Chi Chen; Quan-Zhen Wang; Du Li


Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
239 KB
Volume
66
Category
Article
ISSN
0362-546X

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We are concerned with quasilinear partial differential equations of elliptic type which are degenerate; in particular we investigate the range of such quasilinear differential operators and properties of the solution operator. For elliptic problems which are semilinear in nature, much has been accom

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The method of generalized quasilinearization is extended to semilinear elliptic problems employing both the classical and variational approaches. The results discussed are very general and include several special cases of interest.

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Strong solvability in the Sobolev space W 2 p is proved for the oblique derivative problem almost everywhere in โˆ‚u/โˆ‚ + ฯƒ x u = ฯ• x in the trace sense on โˆ‚ in the case when the vector field x has a contact of infinite order with โˆ‚ at the points of some non-empty subset E โŠ‚ โˆ‚ .