## Journal of Integral Equations and Applications

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

### On some classes of elliptic systems with fractional boundary relaxation

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 27 June 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.jiea/1561601027

**Digital Object Identifier**

doi:10.1216/JIE-2019-31-1-85

**Mathematical Reviews number (MathSciNet)**

MR3974984

**Zentralblatt MATH identifier**

07080016

**Subjects**

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

**Keywords**

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

#### Citation

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. https://projecteuclid.org/euclid.jiea/1561601027