A Harnack's inequality for mixed type evolution equations
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- 作者：Fabio Paronetto ; fabio.paronetto@unipd.it" class="auth_mail" title="E-mail the corresponding author
- 关键词：35B65 ; 35M10 ; 35B50 ; 35B45 ; 35J62 ; 35K65 ; 35J70
- 刊名：Journal of Differential Equations
- 出版年：2016
- 出版时间：15 March 2016
- 年：2016
- 卷：260
- 期：6
- 页码：5259-5355
- 全文大小：935 K
文摘
We define a homogeneous parabolic De Giorgi classes of order 2 which suits a mixed type class of evolution equations whose simplest example is 
where μ can be positive, null and negative, so in particular elliptic–parabolic and forward–backward parabolic equations are included. For functions belonging to this class we prove local boundedness and show a Harnack inequality which, as by-products, gives Hölder-continuity, in particular in the interface I where μ changes sign, and a maximum principle.
where μ can be positive, null and negative, so in particular elliptic–parabolic and forward–backward parabolic equations are included. For functions belonging to this class we prove local boundedness and show a Harnack inequality which, as by-products, gives Hölder-continuity, in particular in the interface I where μ changes sign, and a maximum principle.