A Saint-Venant type principle for Dirichlet forms on discontinuous media
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M. Biroli -U. Mosco,Formes de Dirichlet et estimations structurelles dans les milieux discontinus, C. R. Acad. Sci. Paris A,313 (1991), pp. 593–598.
M. Biroli -U. Mosco,Sobolev inequalities for Dirichlet forms on homogeneous spaces, inBounary Value Problems for Partial Differential Equations and Applications, Essais for 70th Birthday of E. Magenes, edited by C. Baiocchi e J. L. Lions, Masson, Paris (1993), pp. 305–311.
M. Biroli -U. Mosco,Wiener criterion and potential estimates for obstacle problems relative to degenerate elliptic operators, Ann. Mat. Pura Appl., (IV),159 (1991), pp. 255–281.
J. M. Bony,Opérateurs elliptiques dégénérés associés aux axiomatiques de la théorie du potentiel, Corso C.I.M.E. Potential Theories, Ed. Cremonese, Roma (1970), pp. 69–120.
N. Burger,Espace des fonctions à variation moyenne bornée sur un espace de nature homogène, C.R. Acad. Se. Paris A,286 (1978), pp. 139–142.
A. P. Calderon,Inequalities for the maximal function relative to a metric, Studia Math.,57 (1975), pp. 297–306.
R. R. Coifman -G. Weiss,Analyse harmonique non commutative sur certains espaces homogènes, Lecture Notes in Math.,242, Springer-Verlag, Berlin-Heidelberg-New York (1971).
J. Deny,Méthodes hilbertiennes et théorie du potentiel, C.I.M.E., Ed. Cremonese, Roma (1970), pp. 121–203.
E. Fabes -D. Jerison -C. Kenig,The Wiener test for degenerate elliptic equations, Ann. Inst. Fourier,3 (1982), pp. 151–183.
E. Fabes -C. Kenig -R. Serapioni,The local regularity of solutions of degenerate elliptic equations, Comm. Part. Diff. Eq.,7 (1982), pp. 77–116.
C. L. Fefferman -D. Phong,Subelliptic eigenvalue problems,Conference on Harmonic analysis, Chicago, edited by W. Becker et al., Wadsworth (1981), pp. 590–606.
C. L. Fefferman -A. Sanchez Calle,Fundamental solution for second order subelliptic operators, Ann. Math.,124 (1986), pp. 247–272.
G. Fichera,Sulle equazioni differenziali lineari del 2∘ordine ellittico-paraboliche, Atti Acc. Naz. Lincei, Mem. Sez. I (8),5 (1956), pp. 1–30.
G. Fichera,Premessa ad una teoria generale dei problemi al contorno per le equazioni differenziali, Corso Ist. Alta Matematica, Libreria Eredi V. Veschi, Roma (1958).
B. Franchi -E. Lanconelli,An embedding theorem for Sobolev spaces related to non smooth vector fields and Harnack inequality, Comm. Part. Diff. Eq.,9 (1984), pp. 1237–1264.
B. Franchi -R. Serapioni,Pointwise estimates for a class of degenerate elliptic operators: a geometrical approach, Ann. Sc. Norm. sup. Pisa,14, 4 (1987), pp. 527–569.
M. Fukushima,Dirichlet Forms and Markov Processes, North-Holland Math.,23, North-Holland and Kodansha, Amsterdam (1980).
D. Gilbarg -N. S. Trudinger,Elliptic partial differential equations of second order, Grund. Math. Wiss,234, Springer-Verlag, Berlin-Heidelberg-New York (1977).
D. Jerison,The Poincaré inequality for vector fields satisfying an Hörmander's condition, Duke Math. J.,53, 2 (1986), pp. 503–523.
D. Jerison -A. Sanchez Calle,Subelliptic second order differential operators, Lecture Notes in Math.,1277, Springer-Verlag, Berlin-Heidelberg-New York (1987), pp. 46–77.
J. J. Kohn -L. Nirenberg,Degenerate elliptic equations of second order, Comm. Pure Appl. Math.,20 (1967), pp. 797–872.
S. Kosuoka -D. Stroock,Applications of Malliavin calculus, III, J. Fac. Sc. Univ. Tokyo, Sec. IA Math.,34 (1987), pp. 391–442.
Y. Lejean,Measure associées à une forme de Dirichlet: Applications, Bull. Soc. Math. France,106 (1978), pp. 61–112.
U. Mosco,Wiener criterion and potential estimates for the obstacle problem, Indiana Univ. Math. J.,3, 36 (1987), pp. 455–494.
J. Moser,On Harnack's inequality for elliptic differential equations, Comm. Pure Appl. Math.,14 (1961), pp. 377–591.
M. K. V. Murthy -G. Stampacchia,Boundary value problems for some degenerate elliptic operators, Ann. Mat. Pura Appl.,80 (1968), pp. 1–122.
A. Nagel -E. Stein -S. Weinger,Balls and metrics defined by vector fields I: Basic properties, Acta Math.,155 (1985), pp. 103–147.
O. A. Oleinik -E. V. Radkevic,Second Order Equations with Nonnegative Characteristic Form, A.M.S., Plenum Press, New York, London (1979).
L. P. Rotschild -E. Stein,Hypoelliptic differential operators and nilpotent groups, Acta Math.,137 (1976), pp. 247–320.
L. Saloff-Coste,A note on Poincaré, Sobolev and Harnack inequalities, Duke Math. J., Int. Math. Res. Notices,2 (1992), pp. 27–38.
A. Sanchez Calle,Fundamental solutions and geometry of square of vector fields, Inv. Math.,78 (1984), pp. 143–160.
M. L. Silverstein,Symmetric Markov Processes, Lecture Notes in Math.,426, Springer-Verlag, Berlin-Heidelberg-New York (1974).
M. L. Silverstein,Boundary Theory for Symmetric Markov Processes, Lecture Notes in Math.,516, Springer-Verlag, Berlin-Heidelberg-New York (1976).
G. Stampacchia,Équations elliptiques du second ordre à coéfficients discontinus, Les. Presses de l'Université de Montréal, Montréal (1966).