The Green function for uniformly elliptic equations. (English) Zbl 0485.35031


35J15 Second-order elliptic equations
35C15 Integral representations of solutions to PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
Full Text: DOI EuDML


[1] S. Campanato: Equazioni ellitiche del IIo ordine e spaziL (2,?). Ann. di Mat. Pura e Appl.69, 321-381 (1965) · Zbl 0145.36603
[2] J. Frehse: Capacity Methods in the Theory of Partial Differential Equations. Jber. d. Dt. Math.-Verein84 (1982), 1-44 · Zbl 0486.35002
[3] M. Giaquinta et S. Hildebrandt: Estimation ? priori des solutions faibles de certains syst?mes non lin?aires elliptiques. Seminaire Goulaouic-Meyer-Schwartz 1980-1981, Expos? no XVII. Ecole polytechnique. Centre de math?matiques, Palaiseau
[4] M. Gr?ter: Die Greensche Funktion f?r elliptische Differentialoperatoren mit L?-Koeffizienten. Diplomarbeit, Bonn (1976)
[5] S. Hildebrandt, J. Jost and K.-O. Widman: Harmonic mappings and minimal submanifolds. Inventiones math.62, 269-298 (1980) · Zbl 0446.58006
[6] S. Hildebrandt, H. Kaul and K.-O. Widman: An existence theorem for harmonic mappings of Riemannian manifolds. Acta math.138, 1-16(1977) · Zbl 0356.53015
[7] S. Hildebrandt and K.-O. Widman: Some regularity results for quasilinear elliptic systems of second order, Math.Z.142, 67-86 (1975) · Zbl 0317.35040
[8] S. Hildebrandt and K.-O. Widman: On the H?lder continuity of weak solutions of quasilinear elliptic systems of second order. Ann. Scuola Norm. Sup. Pisa (IV),4, 145-178 (1977) · Zbl 0353.35013
[9] S. Hildebrandt and K.-O. Widman: S?tze vom Liouvilleschen Typ f?r quasilineare elliptische Gleichungen und Systeme. Nachr. Akad. Wiss. G?ttingen, II. Math.- Phys. Klasse, Nr.4, 41-59 (1979) · Zbl 0426.35037
[10] S. Hildebrandt and K.-O. Widman: Variational inequalities for vector-valued functions. J. reine angew. Math.309, 191-220 (1979) · Zbl 0408.49012
[11] P.-A. Ivert: A priori Schranken f?r die Ableitungen der L?sungen gewisser elliptischer Differentialgleichungssysteme, man. math.23, 279-294 (1978) · Zbl 0374.35021
[12] P.-A. Ivert: Regularit?tsuntersuchungen von L?sungen elliptischer Systeme von quasilinearen Differentialgleichungen zweiter Ordnung, man. math.30, 53-88 (1979) · Zbl 0429.35033
[13] D. Kinderlehrer and G. Stampacchia: An Introduction to Variational Inequalities and Their Applications. New York-London-Toronto-Sydney-San Francisco. Academic Press 1980 · Zbl 0457.35001
[14] H. Lewy and G. Stampacchia: On the regularity of the solution of a Variational inequality. Comm. Pure Appl. Math.22, 153-188 (1969) · Zbl 0167.11501
[15] W. Littman, G. Stampacchia and H.F. Weinberger: Regular points for elliptic equations with discontinuous coefficients. Ann. Scuola Norm. Sup. Pisa (III),17, 43-77 (1963) · Zbl 0116.30302
[16] J. Moser: On Harnack’s theorem for elliptic differential equations. Comm. Pure Appl. Math.14, 577-591 (1961) · Zbl 0111.09302
[17] K.-O. Widman: On the boundary behaviour of solutions to a class of elliptic partial differential equations. Ark. f?r Mat. 6.26, 485-533 (1966) · Zbl 0166.37702
[18] K.-O. Widman: The singularity of the Green function for non-uniformly elliptic partial differential equations with discontinuous coefficients. Uppsala University, Department of Mathematics 12 (1970) · Zbl 0217.12802
[19] K.-O. Widman: Regular points for a class of degenerating elliptic partial differential equations. Uppsala University, Department of Mathematics 29 (1971)
[20] K.-O. Widman: Inequalities for Green functions of second order elliptic operators. Link?ping University, Department of Mathematics 8 (1972)
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.