On an initial-boundary value problem for the equation w t = w x x - x w y

Carlo Domenico Pagani

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1975)

  • Volume: 2, Issue: 2, page 219-263
  • ISSN: 0391-173X

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Pagani, Carlo Domenico. "On an initial-boundary value problem for the equation $w_t = w_{xx} - xw_y$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 2.2 (1975): 219-263. <http://eudml.org/doc/83688>.

@article{Pagani1975,
author = {Pagani, Carlo Domenico},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {2},
pages = {219-263},
publisher = {Scuola normale superiore},
title = {On an initial-boundary value problem for the equation $w_t = w_\{xx\} - xw_y$},
url = {http://eudml.org/doc/83688},
volume = {2},
year = {1975},
}

TY - JOUR
AU - Pagani, Carlo Domenico
TI - On an initial-boundary value problem for the equation $w_t = w_{xx} - xw_y$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1975
PB - Scuola normale superiore
VL - 2
IS - 2
SP - 219
EP - 263
LA - eng
UR - http://eudml.org/doc/83688
ER -

References

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  1. [1] W. Fleming, A problem of random accelerations, U.S. Army Math. Center, Univ. of Wisconsin, M.R.C. Rep., 1963. 
  2. [2] T.G. Gen, Ultraparabolic equations, Dokl. Akad. Nauk SSSR, 151 (1963), pp. 265-268; Soviet Math. Dokl., 4 (1963), pp. 979-982. Zbl0128.32503MR151731
  3. [3] J.J. Kohn - L. Nirenberg, Degenerate elliptic -parabolic equations of second order, Comm. Pure and Appl. Math., 20 (1967), pp. 797-872. Zbl0153.14503MR234118
  4. [4] A.N. Kolmogorov, Zufällige Bewegungen, Ann. of Math., 35 (1934), pp. 116-117. MR1503147JFM60.1159.01
  5. [5] A.M. Il'in, On a class of ultraparabolic equations, Dokl. Akad. Nauk SSSR, 159 (1964), pp. 1214-1217; Soviet Math. Dokl., 5 (1964), pp. 1673-1676. Zbl0173.37702MR171084
  6. [6] O.A. Ole, On the smoothness of solutions of degenerate elliptic and parabolic equations, Dokl. Akad. Nauk SSSR, 163 (1965), pp. 577-580; Soviet Math. Dokl., 6 (1965), pp. 972-975. Zbl0142.37201MR200595
  7. [7] O.A. Ole - E.V. Radkevi, Second order equations with nonnegative characteristic form, AMS and Plenum Press, New York, 1973. MR457908
  8. [8] C.D. Pagani, Su un problema di valori iniziali per una equazione parabolica singolare, Rend. Ist. Lombardo, 103 (1969), pp. 618-653. Zbl0193.38901MR262698
  9. [9] C.D. Pagani, On the parabolic equation sgn (x) |x|x uv— uxx = 0 and a related one, Ann. Mat. Pura e Appl., 99 (1974), pp. 333-399. Zbl0274.35038MR415070
  10. [10] C.D. Pagani - G. Talenti, On a forward-backward parabolic equation, Ann. Mat. Pura e Appl., 90 (1971), pp. 1-58. Zbl0238.35043MR313635
  11. [11] Ja. I. Šatyro, The first boundary value problem for a certain ultraparabolic equation, in russian, Differencial'nye Uravnenija, 7 (1971), pp. 1089-1096. Zbl0229.35048MR308597
  12. [12] G. Talenti, Sulle equazioni integrali di Wiener-Hopf, Boll. U.M.I., (4), 7, Suppl. fasc. 1 (1973), pp. 18-118. Zbl0281.45007MR338713
  13. [13] M. Weber, The fundamental solution of a degenerate partial differential equation of parabolic type, Trans. Amer. Math. Soc., 71 (1951), pp. 24-37. Zbl0043.09901MR42035
  14. [14] K. Yosida, Functional analysis, Springer-Verlag, Berlin, 1965. Zbl0126.11504
  15. [15] G.H. Hardy - J.E. Littlewood - G. Polya, Inequalities, University Press, Cambridge, 1952. Zbl0047.05302MR46395

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