Comparison theorems for temperatures in noncylindrical domains

Eugene B. Fabes; Nicola Garofalo; Sandro Salsa

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1984)

  • Volume: 77, Issue: 1-2, page 1-12
  • ISSN: 1120-6330

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Fabes, Eugene B., Garofalo, Nicola, and Salsa, Sandro. "Comparison theorems for temperatures in noncylindrical domains." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 77.1-2 (1984): 1-12. <http://eudml.org/doc/287488>.

@article{Fabes1984,
author = {Fabes, Eugene B., Garofalo, Nicola, Salsa, Sandro},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {comparison theorems; divergence type parabolic equations; Lipschitz cylinders; heat equation; interior Harnack principle; positive solutions; Harnack inequality},
language = {eng},
month = {7},
number = {1-2},
pages = {1-12},
publisher = {Accademia Nazionale dei Lincei},
title = {Comparison theorems for temperatures in noncylindrical domains},
url = {http://eudml.org/doc/287488},
volume = {77},
year = {1984},
}

TY - JOUR
AU - Fabes, Eugene B.
AU - Garofalo, Nicola
AU - Salsa, Sandro
TI - Comparison theorems for temperatures in noncylindrical domains
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1984/7//
PB - Accademia Nazionale dei Lincei
VL - 77
IS - 1-2
SP - 1
EP - 12
LA - eng
KW - comparison theorems; divergence type parabolic equations; Lipschitz cylinders; heat equation; interior Harnack principle; positive solutions; Harnack inequality
UR - http://eudml.org/doc/287488
ER -

References

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  1. BAUMAN, P.E. (1982) - Properties of non-negative solutions of second-order elliptic equations and their adjoints, «Univ. of Minnesota», Ph.D Thesis, June. MR2632044
  2. CAFFARELLI, L., FABES, E.B., MORTOLA, S. and SALSA, S. (1981) - Boundary behavior of non-negative solutions of elliptic operators in divergence form, «Indiana Univ. Math. Journal», 30, 621-640. Zbl0512.35038MR620271DOI10.1512/iumj.1981.30.30049
  3. FABES, E.B., GAROFALO, N. and SALSA, S. - A Backward Harnack inequality and Fatou theorem for non-negative solutions of parabolic equations, «Illinois Journal of Mathematics », to appear. Zbl0625.35006MR857210
  4. FRIEDMAN, A. (1964) - PDE of parabolic type, Prentice Hall. MR181836
  5. GAROFALO, N. - Second order parabolic equations in non-variational form : Boundary Harnack Principle and comparison theorems for non-negative solutions, «Annali di Mat. Pura ed Applicata», to appear. Zbl0574.35039MR779547DOI10.1007/BF01762548
  6. JONES, F.B. and Tu, C.C. (1972) - On the existence of kernel functions for the heat equation, «Indiana Univ. Math. Journal», 21, 857-876. Zbl0239.35053MR294902
  7. 1 KEMPER, J.T. (1972) - Temperatures in several variables: kernel functions, representations, and parabolic boundary values, «TAMS», 167, 243-262. Zbl0238.35039MR294903
  8. KEMPER, J.T. (1972) - A boundary Harnack Principle for Liptchitz domains and the principle of positive singularities, «CPAM», XXV, 247-255. Zbl0226.31007MR293114
  9. MOSER, J. (1964) - A Harnack inequality for parabolic differential equations, «CPAM», XVII, 101-134. Zbl0149.06902MR159139
  10. SALSA, S. (1981) - Some properties of non-negative solutions of parabolic differential operators, «Annali di Mat. Pura ed Applicata», 128, 193-206. Zbl0477.35049MR640782DOI10.1007/BF01789473
  11. Wu, J.M. (1979) - On parabolic measures and superparabolie functions, «TAMS », 251, 171-185. Zbl0426.35044MR531974DOI10.2307/1998688

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