An A Priori Estimate for the Modulus of Continuity of a Generalized Solution of a Parabolic Equation of Divergent Form with Degeneracy

• Date: 2001
• Main Authors: Verba, I. I., Kolody, I. M., Верба, И. И., Колодий, И. М.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2001
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4234
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study parabolic equations of divergent form with degeneracy λ(x) with respect to the space variable. We establish an a priori estimate of the Hölder norm of generalized solutions. The problem is considered in parabolic cylinders having a special time dimension induced by the degeneracy λ(x).