Strong maximum principles for implicit parabolic functional-differential problems together with initial inequalities
Abstract
The aim of the paper is to give strong maximum principles for implicit non-linear parabolic functional-differential problems together with initial inequalities in relatively arbitrary (n+1)-dimensional time-space sets more general than cylindrical domains.
References
P. Besala, An extension of the strong maximum principle for parabolic equations, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 19 (1971), 1003-1006.
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L. Byszewski, Strong maximum principle for implicit nonlinear parabolic functional-differential inequalities in arbitrary domains, Univ. Iagell. Acta Math. 24 (1984), 327-339.
##plugins.generic.googleScholarLinks.settings.viewInGS##
L. Byszewski, Strong maximum and minimum principles for parabolic functional-differential problems with initial inequalities u(t0, x) ≤(≥)K, Ann. Polon. Math. 52 (1990), 187-194.
##plugins.generic.googleScholarLinks.settings.viewInGS##
R. Redheffer, W. Walter, Das Maximumprinzip in unbeschränkten Gebieten für parabolische Ungleichungen mit Funktionalen, Math. Ann. 226 (1977), 155-170.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Szarski, Differential Inequalities, PWN, Warszawa, 1967.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Szarski, Strong maximum principle for non-linear parabolic differentialfunctional inequalities in arbitrary domains, Ann. Polon. Math. 29 (1974), 207- 217.
##plugins.generic.googleScholarLinks.settings.viewInGS##
J. Szarski, Inifinite systems for parabolic differential-functional inequalities, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), 471-481.
##plugins.generic.googleScholarLinks.settings.viewInGS##
W. Walter, Differential and Integral Inequalities, Springer–Verlag, Berlin – Heidelberg – New York, 1970.
##plugins.generic.googleScholarLinks.settings.viewInGS##
N. Yoshida, Maximum principles for implicit parabolic equations, Proc. Japan Acad. 49 (1973), 785-788.
##plugins.generic.googleScholarLinks.settings.viewInGS##
