Degenerate integrodifferential equations of parabolic type with Robin boundary conditions: L^p-theory

详细信息    查看全文

• 作者：Angelo Favini ^{angelo.favini@unibo.it" class="auth_mail" title="E-mail the corresponding author} ; Alfredo Lorenzi ; Hiroki Tanabe
• 关键词：Direct problems of parabolic type for time depending operator coefficients in Banach spaces ; Linear parabolic integro-differential equations ; Existence and uniqueness of solutions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：447
• 期：1
• 页码：579-665
• 全文大小：1096 K

文摘

The aim of this paper consists in solving integrodifferential problem of type (1.1)–(1.2) that may degenerate both in space and time. More precisely, {M_p(t)}_t∈[0,T]${\{M_p(t)\}}_{t\in [0,T]}$ is a family of multiplication operators related to a scalar function m(t,x)$m(t,x)$ that may vanish, while {L_p(t)}_t∈[0,T]${\{L_p(t)\}}_{t\in [0,T]}$ is the realization of a family of linear second-order differential operators, with smooth coefficients, {L(t)}_t∈[0,T]${\{\mathcal{L}(t)\}}_{t\in [0,T]}$, {L_p(t)}$\{L_p(t)\}$ being invertible for all t∈[0,T]$t\in [0,T]$. Moreover, {B_p(t,s)}_{t,s∈[0,T],s≤t}${\{B_p(t,s)\}}_{t,s\in [0,T],s\le t}$ is the realization of a family {B(t,s)}_{t∈[0,T],s≤t}${\{\mathcal{B}(t,s)\}}_{t\in [0,T],s\le t}$ of linear second-order differential operators with smooth coefficients. Finally, the scalar functions a and b   are such that 1/a$1/a$ and b/a$b/a$ are Hölder-continuous with suitable Hölder exponents.