×

On the definition of ellipticity for systems of partial differential equations. (English) Zbl 0746.35012

The paper is devoted to the study of ellipticity of partial differential equations and systems. In particular the author studies the relationship between the concepts introduced by A. Douglis and L. Nirenberg [Commun. Pure Appl. Math. 8, 503–538 (1955; Zbl 0066.08002)] and by M. H. Protter [Pitman Res. Notes Math., Ser. 175, 68–81 (1988; Zbl 0669.35031)].

MSC:

35J56 Boundary value problems for first-order elliptic systems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Agmon, S, The Lp approach to the Dirichlet problem, Ann. scuola norm. sup. Pisa cl. sci. (3), 13, 405-448, (1959) · Zbl 0093.10601
[2] Agmon, S, Lectures on elliptic boundary value problems, (1965), Van Nostrand Princeton · Zbl 0151.20203
[3] Agmon, S; Douglis, A; Nirenberg, L, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II, Comm. pure appl. math., 17, 35-92, (1964) · Zbl 0123.28706
[4] Douglis, A; Nirenberg, L, Interior estimates for elliptic systems of partial differential equations, Comm. pure appl. math., 8, 503-538, (1955) · Zbl 0066.08002
[5] Hile, G.N; Protter, M.H, Maximum principles for a class of first-order elliptic systems, J. differential equations, 24, 136-151, (1977) · Zbl 0351.35007
[6] Morrey, C.B, Second order elliptic systems of differential equations, Ann. of math. stud., 33, 101-159, (1954) · Zbl 0057.08301
[7] Morrey, C.B, Multiple integrals in the calculus of variations, (1966), Springer-Verlag New York · Zbl 0142.38701
[8] Protter, M.H, Overdetermined first order elliptic systems, (), 68-81 · Zbl 0669.35031
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.