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Some regularity results for quasilinear elliptic systems of second order. (English) Zbl 0317.35040

35J60 Nonlinear elliptic equations
35D10 Regularity of generalized solutions of PDE (MSC2000)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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[1] Alber’, S. I.: The topology of functional manifolds and the calculus of variations in the large. Russ. math. Surveys25 (4), 51-117 (1970) · Zbl 0222.58002
[2] Courant, R.: Dirichlet’s principle, conformal mapping, and minimal surfaces. New York: Interscience 1950 · Zbl 0040.34603
[3] De Giorgi, E.: Un esempio di estremali discontinue per un problema variazionale di tipo ellitico. Boll. Un. mat. Ital. IV. Ser.1, 135-138 (1968) · Zbl 0155.17603
[4] Eells, J., Sampson, J. H.: Harmonic mappings of Riemannian manifolds. Amer. J. Math.86, 109-160 (1964) · Zbl 0122.40102
[5] Frehse, J.: A discontinuous solution of a mildly nonlinear elliptic system. Math. Z.134, 229-230 (1973) · Zbl 0267.35038
[6] Giusti, E.: Regolaritá parziale delle soluzioni di sistemi ellitici quasi-lineari de ordine arbitrario. Ann. Scuola norm. sup. Pisa, Sci. fis. mat., III. Ser.23, 115-141 (1969). Cf. also the same Journal Vol.27, 161-166 (1973) · Zbl 0175.40102
[7] Giusti, E., Miranda, M.: Un esempio di soluzioni per un problema di minimo relativo ad un integrale regolare del calcolo delle variazioni. Boll. Un. mat. Ital. IV. Ser.2, 1-8 (1968) · Zbl 0155.44501
[8] Giusti, E., Miranda, M.: Sulla regolaritá delle soluzioni deboli di una classe di sistemi ellitici quasi-lineari. Arch. rat. Mech. Anal.31, 173-184 (1968) · Zbl 0167.10703
[9] Gulliver, R.: Existence of surfaces with prescribed mean curvature vector. Math. Z.131, 117-140 (1973) · Zbl 0261.53041
[10] Hartman, P.: On homotopic harmonic maps. Canadian J. Math.19, 673-687 (1967) · Zbl 0148.42404
[11] Heinz, E.: On certain nonlinear elliptic differential equations and univalent mappings. J. Analyse math.5, 197-272 (1956/57) · Zbl 0085.08701
[12] Heinz, E.: Existence theorems for one-to-one mappings associated with elliptic systems of second order. I, II. J. Analyse math.15, 325-352 (1965);17, 145-184 (1966) · Zbl 0137.07202
[13] Heinz, E.: A-priori-Abschätzungen für isometrische Einbettungen zweidimensionaler Riemannscher Mannigfaltigkeiten in dreidimensionale Riemannsche Räume. Math. Z.100, 1-16 (1967) · Zbl 0158.40105
[14] Heinz, E., Hildebrandt, S.: The number of branch points of surfaces of bounded mean curvature. J. Diff. Geometry4, 227-235 (1970) · Zbl 0195.23003
[15] Hildebrandt, S., Kaul, H.: Two-dimensional variational problems with obstructions, and Plateau’s problem forH-surfaces in a Riemannian manifold. Commun. pure appl. Math.25, 187-223 (1972) · Zbl 0245.53006
[16] Hildebrandt, S., Widman, K.-O.: On a theorem of Lady?enskaya and Ural’ceva. Dept. Math. Linköping Report
[17] Lady?enskaya, O. A., Ural’ceva, N. N.: Linear and quasilinear elliptic equations. New York and London: Academic Press 1968. (English translation of the 1st Russian edition 1964)
[18] Lady?enskaya, O. A., Ural’ceva, N. N.: Linear and quasilinear elliptic equations. Second Russian Edition. Moscow: Nauka 1973
[19] Littman, W., Stampacchia, G., Weinberger, H. F.: Regular points for elliptic equations with discontinuous coefficients. Ann. Scuola norm, sup. Pisa, Sci. fis. mat., III. Ser.17, 43-77 (1963) · Zbl 0116.30302
[20] Morrey, C. B.: Multiple integrals in the calculus of variations. Berlin-Heidelberg-New York: Springer 1966 · Zbl 0142.38701
[21] Morrey, C. B.: Partial regularity results for non-linear elliptic systems. J. Math. Mech.17, 649-670 (1968) · Zbl 0175.11901
[22] Oskolkov, A. P.: Prior estimates of the first derivatives for two-dimensional quasilinear strongly elliptic systems. Proc. Steklov Inst. Math.92, 219-232 (1966) · Zbl 0165.12002
[23] Solonnikov, V. A.: O matricah Grina dlya ellipti?eskih kraevyh zada?. I, II. Trudy mat. Inst. Steklov110, 107-145 (1970);116, 181-216 (1971)
[24] Sperner, E., Jr.: Symmetrisierung für Funktionen mehrerer reeller Variablen. Manuscripta math.11, 159-170 (1974) · Zbl 0268.26011
[25] Sperner, E., Jr.: Zur Regularitätstheorie gewisser Systeme nichtlinearer elliptischer Differentialgleichungen. Dissertation, Bonn 1975
[26] Stampacchia, G.: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinues. Ann. Inst. Fourier15, 189-258 (1965) · Zbl 0151.15401
[27] Tomi, F.: Ein einfacher Beweis eines Regularitätssatzes für schwache Lösungen gewisser elliptischer Systeme. Math. Z.112, 214-218 (1969). · Zbl 0177.14704
[28] Tomi, F.: Bemerkungen zum Regularitätsproblem der Gleichung vorgeschriebener mittlerer Krümmung. Math. Z.134, 323-326 (1973) · Zbl 0258.35022
[29] Uhlenbeck, K.: The Regularity of Polyharmonic Maps. Preprint · Zbl 0208.12802
[30] Von Wahl, W.: Einige neue innere Abschätzungen für nichtlineare elliptische Gleichungen und Systeme. Math. Z.134, 119-128 (1973) · Zbl 0269.35043
[31] Wente, H. C.: An existence theorem for surfaces of constant mean curvature. J. math. Analysis Appl.26, 318-344 (1969) · Zbl 0181.11501
[32] Wente, H. C.: The differential equation ?x=2H(x u ?x v ) with vanishing boundary values. Preprint · Zbl 0313.35030
[33] Widman, K. O.: The singularity of the Green function for non-uniformly elliptic partial differential equations with discontinuous coefficients. Uppsala University, Dec. 1970
[34] Widman, K. O.: Hölder continuity of solutions of elliptic systems. Manuscripta math.5, 299-308 (1971) · Zbl 0223.35044
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