Non-negative solutions of linear parabolic equations

Aronson, D. G.

Aronson, D. G.

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 22 (1968) no. 4, pp. 607-694.

MR 435594 | Zbl 0182.13802 | 15 citations dans Numdam

⇒ complété par Non-negative solutions of linear parabolic equations : an addendum

@article{ASNSP_1968_3_22_4_607_0,
     author = {Aronson, D. G.},
     title = {Non-negative solutions of linear parabolic equations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {607--694},
     publisher = {Scuola normale superiore},
     volume = {Ser. 3, 22},
     number = {4},
     year = {1968},
     zbl = {0182.13802},
     mrnumber = {435594},
     language = {en},
     url = {archive.numdam.org/item/ASNSP_1968_3_22_4_607_0/}
}

Aronson, D. G. Non-negative solutions of linear parabolic equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 22 (1968) no. 4, pp. 607-694. http://archive.numdam.org/item/ASNSP_1968_3_22_4_607_0/

Bibliographie

[1] D.G. Aronson, On the Green's function for second order parabolic equations with discontinuous coefficients, Bulletin of the American Mathematical Society, 69 (1963) 841-847. | MR 155109 | Zbl 0154.11903

[2] D.G. Aronson, Isolated singularities of solutions of second order parabolic equations, Archive for Rational Mechanics and Analysis 19 (1965), 231-238. | MR 179468 | Zbl 0143.13705

[3] D.G. Aronson, Uniqueness of positive weak solution of second order parabolic equations, Annales Polonici Mathematici, 16 (1965), 285-303. | MR 176231 | Zbl 0137.29403

[4] D.G. Aronson, Bounds for the fundamental solution of a parabolic equation, Bulletin of the American Mathematical Society, 73 (1967), 890-896. | MR 217444 | Zbl 0153.42002

[5] D.G. Aronson and P. Besala, Uniqueness of solutions of the Cauchy problem for parabolic equations, Journal of Mathematical Analysis and Applications, 13 (1966), 516-526; 17 (1967), 194-196. | MR 192197 | Zbl 0137.29501

[6] D.G. Aronson and J. Seriun, Local behavior of solutions of quasilinear parabolic equations, Arohive for Rational Mechanics and Analysis, 25 (1967), 81-122. | MR 244638 | Zbl 0154.12001

[7] L. Bers, Topology, Lecture Notes, Courant Institute of Mathematical Sciences, 1956-1957.

[8] S. Bochner and A.E. Taylor, Linear functionals on certain spaces of abstractly-valued functions, Annals of Mathematics, 39 (1938), 913-944. | JFM 64.0383.01 | MR 1503445 | Zbl 0020.37101

[9] Avner Friedman, On the uniqueness of the Cauchy problem for parabolic equations, American Journal of Mathematics, 81 (1959), 503-511. | MR 104907 | Zbl 0086.30001

[10] Avner Friedman, Partial Differential Equations of Parabodic Type, Prentice-Hall, Englewood Cliffs, N. J., 1964. | MR 181836 | Zbl 0144.34903

[11] O. Frostman, Potenciel d'equilibre et capacités des ensembles, Meddel. Lunds Univ. Mat. Sem. 3 (1935), 1-118. | JFM 61.1262.02

[12] A.M. Il'In, A.S. Kalashnikov and O.A. Oleinik, Second order linear equations of parabolic type, Russian Mathematical Surveys, 17, no. 3 (1962), 1-143. | MR 138888

[13] A.V. Ivanov, O.A. Lady, A.L. Treskunov and N.N. Urel'Ceva, Gener-alized solutions of parabolic equations of second order, Trudy Matematičeskogo Instituta imeni V. A. Steklova, 92 (1966), 57-92 (Russian). | Zbl 0152.10703

[14] M Krzyzański, Sur les solutions non négatives de l'équation linéaire normale parabolique, Revue Ronmaine de Mathématiques Pures et Appliqueés, 9 (1964), 393-408. | MR 182813 | Zbl 0168.35903

[15] O.A. Ladyženskaja, V.A. Solonnikov and N.N. Urel'Ceva, Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow, 1967 (Russian).

[16] J. Nash, Continuity of solutions of parabolic and elliptic equations, American Journal of Mathematics, 80 (1958), 931-954. | MR 100158 | Zbl 0096.06902

[17] F. Riesz and B. Sz-Nagy, Functional Analysis, Unger, New York, 1955. | MR 71727

[18] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966. | MR 210528 | Zbl 0142.01701

[19] J. Serrin, A uniqueness theorem for the parabolic equation ut = a (x) uxx + b (x) ux, +c(x)u, Bulletin of the American Mathematical Society 60 (1954), 344 (Abstract).

[20] J. Serrin, Introduction to Differentiation Theory, Lecture notes, University of Minnesota, School of Mathematics, 1965.

[21] N.S. Trudinger, Pointwise estimates and quasilinear parabolic equations, Communications on Pure and Applied Mathematics, 21 (1968), 206-226. | MR 226168 | Zbl 0159.39303

[22] D.V. Widder, Positive temperature, on the infinite rod, Transactions of the American Mathematical Society, 55 (1944), 85-95. | MR 9795 | Zbl 0061.22303