1-DIMENSIONAL HARNACK ESTIMATES

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DÜZGÜN F. G., GIANAZZA U., Vespri V.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, cilt.9, sa.3, ss.675-685, 2016 (SCI-Expanded, Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 9 Sayı: 3
• Basım Tarihi: 2016
• Doi Numarası: 10.3934/dcdss.2016021
• Dergi Adı: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.675-685
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• Hacettepe Üniversitesi Adresli: Evet

Özet

Let u be a non-negative super-solution to a 1-dimensional singular parabolic equation of p-Laplacian type (1 < p < 2). If u is bounded below on a time-segment {y} x (0, T] by a positive number M, then it has a power like decay of order 2 Pp with respect to the space variable x in R x [T/2, T]. This fact, stated quantitatively in Proposition 1.2, is a "sidewise spreading of positivity" of solutions to such singular equations, and can be considered as a form of Harnack inequality. The proof of such an effect is based on geometrical ideas.