Hölder regularity theorem for a class of linear nonuniformly elliptic operators with measurable coefficients

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1. [1] N. Burger, Espace des fonctions à variation moyenne bornée sur un espace de nature homogène, C. R. Acad. Sci. Paris Sér. A, 236 (1978), pp. 139-142. Zbl0368.46037MR467176
2. [2] H. Busemann, The Geometry of Geodesics, Academic Press, New York, 1955. Zbl0112.37002MR75623
3. [3] R.R. Coifman - G. Weiss, Analyse Harmonique Non-Commutative sur Certains Espaces Homogènes, Springer, Berlin - Heidelberg - New York, 1971. Zbl0224.43006MR499948
4. [4] R.R. Coifman - G. Weiss, Extensions of Hardy Spaces and Their Use in Analysis, Bull. Amer. Math. Soc., 83 (1977), pp. 569-645. Zbl0358.30023MR447954
5. [5] E. De Giorgi, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., 3 (3) (1957), pp. 25-43. Zbl0084.31901MR93649
6. [6] E.B. Fabes - C.E. Kenig - R.P. Serapioni, The Local Regularity of Solutions of Degenerate Elliptic Equations, Comm. Partial Differential Equations7 (1) (1982), pp. 77-116. Zbl0498.35042MR643158
7. [7] C. Fefferman - D. Phong, Subelliptic Eigenvalue Problems, Preprint 1981. MR730094
8. [8] B. Franchi - E. Lanconelli, De Giorgi's Theorem for a Class of Strongly Degenerate Elliptic Equations, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 72 (8) (1982), pp. 273-277. Zbl0543.35041MR728257
9. [9] B. Franchi - E. Lanconelli, Une métrique associée à une classe d'opérateurs elliptiques dégénérés, Proceedings of the meeting «Linear Partial and Pseudo Differential Operators », Torino (1982), Rend. Sem. Mat. Univ. e Politec. Torino, to appear. Zbl0553.35033MR728257
10. [10] B. Franchi - E. Lanconelli, An Embedding Theorem for Sobolev Spaces Related to Non-Smooth Vector Fields and Harnack Inequality, to appear. Zbl0589.46023
11. [11] Gilbarg - N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin - Heidelberg - New York, 1977. Zbl0361.35003MR473443
12. [12] L. Hörmander, Hypoelliptic Second-Order Differential Equations, Acta Math.119 (1967), pp. 147-171. Zbl0156.10701MR222474
13. [13] I.M. Kolodii, Qualitative Properties of the Generalized Solutions of Degenerate Elliptic Equations, Ukrain. Math. Z., 27 (1975), pp. 320-328 = Ukrainian Math. J., 27 (1975), pp. 256-263. Zbl0337.35009MR412576
14. [14] S.N. Kruzkov, Certain Properties of Solutions to Elliptic Equations, Dokl. Akad. Nauk SSSR, 150 (1963), pp. 470-473 = Soviet Math. Dokl., 4 (1963), pp. 686-690. Zbl0148.35701MR150442
15. [15] J. Moser, A New Proof of De Giorgi's Theorem Concerning the Regularity Probem for Elliptic Differential Equations, Comm. Pure Appl. Math., 13 (1960), pp. 457-468. Zbl0111.09301MR170091
16. [16] M.K.V. Murthy - G. Stampacchia, Boundary Value Problems for Some Degenerate-Elliptic Operators, Ann. Mat. Pura Appl., 80 (4) (1968), pp. 1-122. Zbl0185.19201MR249828
17. [17] J. Nash, Continuity of Solutions of Parabolic and Elliptic Equations, Amer. J. Math., 80 (1958), pp. 931-954. Zbl0096.06902MR100158
18. [18] N.S. Trudinger, Linear Elliptic Operators with Measurable Coefficients, Ann. Scuola Norm. Sup. Pisa, (3) 27 (1973), pp. 265-308. Zbl0279.35025MR369884

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