Open Access
2019 On some classes of elliptic systems with fractional boundary relaxation
Jan Pruss
J. Integral Equations Applications 31(1): 85-104 (2019). DOI: 10.1216/JIE-2019-31-1-85


Classes of second order, one- or two phase- elliptic systems with time-fractional boundary conditions are studied. It is shown that such problems are well posed in an $L_q$-setting, and stability is considered. The tools employed are sharp results for elliptic boundary and transmission problems and for the resulting Dirichlet-Neumann operators, as well as maximal $L_p$-regularity of evolutionary integral equations, based on modern functional analytic tools like $\mathcal{R} $-boundedness and the operator-valued $\mathcal{H} ^\infty $-functional calculus.


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Jan Pruss. "On some classes of elliptic systems with fractional boundary relaxation." J. Integral Equations Applications 31 (1) 85 - 104, 2019.


Published: 2019
First available in Project Euclid: 27 June 2019

zbMATH: 07080016
MathSciNet: MR3974984
Digital Object Identifier: 10.1216/JIE-2019-31-1-85

Primary: 35J70 , 35K65

Keywords: $\mathcal{H} ^\infty $-calculus , $\mathcal{R} $-boundedness , Dirichlet-Neumann operators , elliptic operators , evolutionary integral equations , fractional derivatives , maximal $L_p$-regularity , Transmission conditions

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

Vol.31 • No. 1 • 2019
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