Journal of Integral Equations and Applications

On some classes of elliptic systems with fractional boundary relaxation

Jan Pruss

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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.

Article information

J. Integral Equations Applications, Volume 31, Number 1 (2019), 85-104.

First available in Project Euclid: 27 June 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J70: Degenerate elliptic equations 35K65: Degenerate parabolic equations

Elliptic operators transmission conditions Dirichlet-Neumann operators fractional derivatives evolutionary integral equations maximal $L_p$-regularity $\mathcal{H} ^\infty $-calculus $\mathcal{R} $-boundedness


Pruss, Jan. On some classes of elliptic systems with fractional boundary relaxation. J. Integral Equations Applications 31 (2019), no. 1, 85--104. doi:10.1216/JIE-2019-31-1-85.

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