On maximum principle for weak subsolutions of degenerate parabolic linear equations

Salvatore Bonafede

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 3, page 417-430
  • ISSN: 0010-2628

Abstract

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Sufficient conditions are obtained so that a weak subsolution of ( 0 . 1 ) , bounded from above on the parabolic boundary of the cylinder Q , turns out to be bounded from above in Q .

How to cite

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Bonafede, Salvatore. "On maximum principle for weak subsolutions of degenerate parabolic linear equations." Commentationes Mathematicae Universitatis Carolinae 35.3 (1994): 417-430. <http://eudml.org/doc/247589>.

@article{Bonafede1994,
abstract = {Sufficient conditions are obtained so that a weak subsolution of $(0.1)$, bounded from above on the parabolic boundary of the cylinder $Q$, turns out to be bounded from above in $Q$.},
author = {Bonafede, Salvatore},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {maximum principle; weak subsolution; degenerate equation; weak subsolution},
language = {eng},
number = {3},
pages = {417-430},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On maximum principle for weak subsolutions of degenerate parabolic linear equations},
url = {http://eudml.org/doc/247589},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Bonafede, Salvatore
TI - On maximum principle for weak subsolutions of degenerate parabolic linear equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 3
SP - 417
EP - 430
AB - Sufficient conditions are obtained so that a weak subsolution of $(0.1)$, bounded from above on the parabolic boundary of the cylinder $Q$, turns out to be bounded from above in $Q$.
LA - eng
KW - maximum principle; weak subsolution; degenerate equation; weak subsolution
UR - http://eudml.org/doc/247589
ER -

References

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  1. Bonafede S., Sottosoluzioni deboli delle equazioni paraboliche lineari del secondo ordine degeneri, Rendiconti del circolo Matematico di Palermo, Serie II, Tomo XXXIX (1990), 132-152. (1990) 
  2. Eklund N.A., Generalized super-solution of parabolic equations, Transaction of the American Mathematical Society 220 (1976), 235-242. (1976) MR0473522
  3. Gagliardo E., Proprieta' di alcune classi di funzioni in piu' variabili, Ricerche di Matematica 7 (1958), 102-137. (1958) Zbl0089.09401MR0102740
  4. Ivanov A.V., Properties of solutions of linear and quasilinear second-order equations with measurable coefficients which are neither strictly nor non uniformly parabolic, Zap. Nauch. Sem. Leningrad Otdel Mat. Inst. Steklov (LOMI) 69 (1977), 45-65 Transl. in Journal of Soviet Math., 10 (1978), pp. 29-43. (1977) MR0603301
  5. Ladyzhenskaya O.A., Ural'tseva N.N., Linear and quasilinear elliptic equations, Academic Press, New York, 1968. Zbl0177.37404MR0244627
  6. Nicolosi F., Sottosoluzioni deboli delle equazioni paraboliche lineari del secondo ordine superiormente limitate, Le Matematiche 28 (1973), 361-378. (1973) MR0364867
  7. Nicolosi F., Soluzioni deboli dei problemi al contorno per operatori parabolici che possono degenerare, Annali di Matematica (4) 125 (1980), 135-155. (1980) Zbl0452.35065MR1553443
  8. Stampacchia G., Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Annal. Inst. Fourier 15 (1965), 189-257. (1965) Zbl0151.15401MR0192177
  9. Troianello G.M., On weak subsolutions for parabolic second-order operators, Comm. in Partial Diff. Equat. 3 (10), 933-948. (10) MR0507123

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