@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/
[1] 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] 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] Uniqueness of positive weak solution of second order parabolic equations, Annales Polonici Mathematici, 16 (1965), 285-303. | MR 176231 | Zbl 0137.29403
,[4] 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] 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
and ,[6] Local behavior of solutions of quasilinear parabolic equations, Arohive for Rational Mechanics and Analysis, 25 (1967), 81-122. | MR 244638 | Zbl 0154.12001
and ,[7] Topology, Lecture Notes, Courant Institute of Mathematical Sciences, 1956-1957.
,[8] 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
and ,[9] On the uniqueness of the Cauchy problem for parabolic equations, American Journal of Mathematics, 81 (1959), 503-511. | MR 104907 | Zbl 0086.30001
,[10] Partial Differential Equations of Parabodic Type, Prentice-Hall, Englewood Cliffs, N. J., 1964. | MR 181836 | Zbl 0144.34903
,[11] Potenciel d'equilibre et capacités des ensembles, Meddel. Lunds Univ. Mat. Sem. 3 (1935), 1-118. | JFM 61.1262.02
,[12] Second order linear equations of parabolic type, Russian Mathematical Surveys, 17, no. 3 (1962), 1-143. | MR 138888
, and ,[13] Gener-alized solutions of parabolic equations of second order, Trudy Matematičeskogo Instituta imeni V. A. Steklova, 92 (1966), 57-92 (Russian). | Zbl 0152.10703
, , and ,[14] 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] Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow, 1967 (Russian).
, and ,[16] Continuity of solutions of parabolic and elliptic equations, American Journal of Mathematics, 80 (1958), 931-954. | MR 100158 | Zbl 0096.06902
,[17] | MR 71727
and , Functional Analysis, Unger, New York, 1955.[18] Real and Complex Analysis, McGraw-Hill, New York, 1966. | MR 210528 | Zbl 0142.01701
,[19] 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] Introduction to Differentiation Theory, Lecture notes, University of Minnesota, School of Mathematics, 1965.
,[21] Pointwise estimates and quasilinear parabolic equations, Communications on Pure and Applied Mathematics, 21 (1968), 206-226. | MR 226168 | Zbl 0159.39303
,[22] Positive temperature, on the infinite rod, Transactions of the American Mathematical Society, 55 (1944), 85-95. | MR 9795 | Zbl 0061.22303
,