Non-negative solutions of linear parabolic equations

D. G. Aronson

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1968)

  • Volume: 22, Issue: 4, page 607-694
  • ISSN: 0391-173X

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Aronson, D. G.. "Non-negative solutions of linear parabolic equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 22.4 (1968): 607-694. <http://eudml.org/doc/83474>.

@article{Aronson1968,
author = {Aronson, D. G.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {partial differential equations},
language = {eng},
number = {4},
pages = {607-694},
publisher = {Scuola normale superiore},
title = {Non-negative solutions of linear parabolic equations},
url = {http://eudml.org/doc/83474},
volume = {22},
year = {1968},
}

TY - JOUR
AU - Aronson, D. G.
TI - Non-negative solutions of linear parabolic equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1968
PB - Scuola normale superiore
VL - 22
IS - 4
SP - 607
EP - 694
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/83474
ER -

References

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  1. [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. Zbl0154.11903MR155109
  2. [2] D.G. Aronson, Isolated singularities of solutions of second order parabolic equations, Archive for Rational Mechanics and Analysis19 (1965), 231-238. Zbl0143.13705MR179468
  3. [3] D.G. Aronson, Uniqueness of positive weak solution of second order parabolic equations, Annales Polonici Mathematici, 16 (1965), 285-303. Zbl0137.29403MR176231
  4. [4] D.G. Aronson, Bounds for the fundamental solution of a parabolic equation, Bulletin of the American Mathematical Society, 73 (1967), 890-896. Zbl0153.42002MR217444
  5. [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. Zbl0137.29501MR192197
  6. [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. Zbl0154.12001MR244638
  7. [7] L. Bers, Topology, Lecture Notes, Courant Institute of Mathematical Sciences, 1956-1957. 
  8. [8] S. Bochner and A.E. Taylor, Linear functionals on certain spaces of abstractly-valued functions, Annals of Mathematics, 39 (1938), 913-944. Zbl0020.37101MR1503445JFM64.0383.01
  9. [9] Avner Friedman, On the uniqueness of the Cauchy problem for parabolic equations, American Journal of Mathematics, 81 (1959), 503-511. Zbl0086.30001MR104907
  10. [10] Avner Friedman, Partial Differential Equations of Parabodic Type, Prentice-Hall, Englewood Cliffs, N. J., 1964. Zbl0144.34903MR181836
  11. [11] O. Frostman, Potenciel d'equilibre et capacités des ensembles, Meddel. Lunds Univ. Mat. Sem.3 (1935), 1-118. JFM61.1262.02
  12. [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. MR138888
  13. [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). Zbl0152.10703
  14. [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. Zbl0168.35903MR182813
  15. [15] O.A. Ladyženskaja, V.A. Solonnikov and N.N. Urel'ceva, Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow, 1967 (Russian). 
  16. [16] J. Nash, Continuity of solutions of parabolic and elliptic equations, American Journal of Mathematics, 80 (1958), 931-954. Zbl0096.06902MR100158
  17. [17] F. Riesz and B. Sz-Nagy, Functional Analysis, Unger, New York, 1955. Zbl0070.10902MR71727
  18. [18] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966. Zbl0142.01701MR210528
  19. [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 Society60 (1954), 344 (Abstract). 
  20. [20] J. Serrin, Introduction to Differentiation Theory, Lecture notes, University of Minnesota, School of Mathematics, 1965. 
  21. [21] N.S. Trudinger, Pointwise estimates and quasilinear parabolic equations, Communications on Pure and Applied Mathematics, 21 (1968), 206-226. Zbl0159.39303MR226168
  22. [22] D.V. Widder, Positive temperature, on the infinite rod, Transactions of the American Mathematical Society, 55 (1944), 85-95. Zbl0061.22303MR9795

Citations in EuDML Documents

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  1. Howard Levine, A global existence-global nonexistence conjecture of Fujita type for a system of degenerate semilinear parabolic equations
  2. Andrzej Rozkosz, Leszek Słomiński, Stochastic representation of reflecting diffusions corresponding to divergence form operators
  3. Xiang Tao, The L p solvability of the Dirichlet problems for parabolic equations
  4. Ermanno Lanconelli, Sul modulo di continuità alla frontiera della soluzione del problema di Dirichlet relativo ad una classe di operatori parabolici
  5. D. G. Aronson, Non-negative solutions of linear parabolic equations : an addendum
  6. Caroline Sweezy, Absolute continuity for elliptic-caloric measures
  7. A. Piatnitski, A. Rybalko, V. Rybalko, Ground states of singularly perturbed convection-diffusion equation with oscillating coefficients
  8. Neil Watson, The representation of smooth functions in terms of the fundamental solution of a linear parabolic equation
  9. Pascal Auscher, Thierry Coulhon, Philippe Tchamitchian, Absence de principe du maximum pour certaines équations paraboliques complexes
  10. E. Brian Davies, Heat kernel bounds for higher order elliptic operators

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