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, Mp(t)t∈[0,T] is a family of multiplication operators related to a scalar function m(t,x) that may vanish, while Lp(t)t∈[0,T] is the realization of a family of linear second-order differential operators, with smooth coefficients, L(t)t∈[0,T], Lp(t) being invertible for all t∈[0,T]. Moreover, Bp(t,s)t,s∈[0,T],s≤t is the realization of a family B(t,s)t∈[0,T],s≤t of linear second-order differential operators with smooth coefficients. Finally, the scalar functions a and b are such that 1/a and b/a are Hölder-continuous with suitable Hölder exponents.
Favini, A., Lorenzi, A., Tanabe, H. (2017). Degenerate integrodifferential equations of parabolic type with Robin boundary conditions: Lp-theory. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 447(1), 579-665 [10.1016/j.jmaa.2016.10.029].
Degenerate integrodifferential equations of parabolic type with Robin boundary conditions: Lp-theory
FAVINI, ANGELO;
2017
Abstract
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, Mp(t)t∈[0,T] is a family of multiplication operators related to a scalar function m(t,x) that may vanish, while Lp(t)t∈[0,T] is the realization of a family of linear second-order differential operators, with smooth coefficients, L(t)t∈[0,T], Lp(t) being invertible for all t∈[0,T]. Moreover, Bp(t,s)t,s∈[0,T],s≤t is the realization of a family B(t,s)t∈[0,T],s≤t of linear second-order differential operators with smooth coefficients. Finally, the scalar functions a and b are such that 1/a and b/a are Hölder-continuous with suitable Hölder exponents.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
