Geodesic
Classical, viscosity and average solutions for PDE’s with nonnegative characteristic form
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 1, pp. 17-28.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We compare several definitions of weak solutions to second order partial differential equations with nonnegative characteristic form.
In questa Nota confrontiamo alcune nozioni di soluzione per equazioni alle derivate parziali del secondo ordine con forma caratteristica semidefinita positiva. 
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Gutiérrez, Cristian E.; Lanconelli, Ermanno. Classical, viscosity and average solutions for PDE’s with nonnegative characteristic form. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 1, pp. 17-28. http://geodesic.mathdoc.fr/item/RLIN_2004_9_15_1_a1/

[1] J.M. Bony, Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptic dégénérés. Ann. Inst. Fourier (Grenoble), 19, 1969, 277-304. | fulltext EuDML | fulltext mini-dml | MR | Zbl

[2] M. BRELOT et al. (eds.), Séminaire de théorie du potentiel, LNM 713. Berlin-Heidelberg-New York 1979.

[3] G. Citti - N. Garofalo - E. Lanconelli, Harnack’s inequality for sum of squares of vector fields plus a potential. Amer. J. Math., 115(3), 1993, 699-734. | DOI | MR | Zbl

[4] W. Fulks, An approximate Gauss mean value theorem. Pacific J. Math., 14, 1964, 513-516. | fulltext mini-dml | MR | Zbl

[5] W. Fulks, A mean value theorem for the heat equation. Proc. Amer. Math. Soc., 17, 1966, 6-11. | MR | Zbl

[6] N. Garofalo - E. Lanconelli, Level sets of the fundamental solution and Harnack inequality for degenerate equations of Kolmogorov type. Trans. Amer. Math. Soc., 321(2), 1990, 775-792. | DOI | MR | Zbl

[7] M. Hansson, Harmonicity of functions satisfying a weak form of the mean value property. Arch. Math. (Basel), 76, 2001, 283-291. | DOI | MR | Zbl

[8] L.P. Kupcov, The mean value property and the maximum principle for second order parabolic equations. Dokl. Akad. Nauk SSSR, 242(3), 1978, 529-532. | MR | Zbl

[9] E. Lanconelli - S. Polidoro, On a class of hypoelliptic evolution operators. Rend. Sem. Mat. Univ. Politec. Torino, 52(1), 1994, 29-63. | MR | Zbl

[10] E. Lanconelli - A. Pascucci, Superparabolic functions related to second order hypoelliptic operators. Potential Anal., 11(3), 1999, 303-323. | DOI | MR | Zbl

[11] C.D. Pagani, Approximation of the solutions to the first boundary value problem for parabolic equations. Confer. Sem. Mat. Univ. Bari, 154, 1978, 26 pp. | MR | Zbl

[12] B. Pini, Sulla soluzione generalizzata di Wiener per il primo problema di valori al contorno nel caso parabolico. Rend. Sem. Mat. Univ. Padova, 23, 1954, 422-434. | fulltext EuDML | fulltext mini-dml | MR | Zbl

[13] C. Pucci - G. Talenti, Elliptic (second-order) partial differential equations with measurable coefficients and approximating integral equations. Advances in Math., 19(1), 1976, 48-105. | MR

[14] S. Ramaswamy, Maximum principle for viscosity sub solutions and viscosity sub solutions of the Laplacian. Rend. Mat. Acc. Lincei, s. 9, v. 4, 1993, 213-217. | fulltext bdim | fulltext EuDML | fulltext mini-dml | MR | Zbl

[15] F. Uguzzoni, A note on a generalized form of the Laplacian and of sub-Laplacians. Arch. Math. (Basel), 80, 2003, 516-524. | DOI | MR | Zbl

[16] N.A. Watson, A theory of subtemperatures in several variables. Proc. London Math. Soc., 26(3), 1973, 385-417. | MR | Zbl