| 1. |
- Mitrea, Irina, et al.
(författare)
-
Interval Analysis Techniques for Boundary Value Problems of Elasticity in Two Dimensions
- 2007
-
Ingår i: Journal of Differential Equations. - : Elsevier BV. - 0022-0396 .- 1090-2732. ; 233:1, s. 181-198
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we prove that the L-2 spectral radius of the traction double layer potential operator associated with the Lame system on an infinite sector in R-2 is within 10(-2) from a certain conjectured value which depends explicitly on the aperture of the sector and the Lame moduli of the system. This type of result is relevant to the spectral radius conjecture, cf., e.g., Problem 3.2.12 in [C.E. Kenig, Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems, CBMS Reg. Conf. Ser. Math., vol. 83, Amer. Math. Soc., Providence, RI, 1994]. The techniques employed in the paper are a blend of classical tools such as Mellin transforms, and Calderon-Zygmund theory, as well as interval analysis-resulting in a computer-aided proof.
|
|
| 2. |
- Mitrea, Irina, et al.
(författare)
-
Invertibility Properties of Singular Integral Operators Associated with the Lam, and Stokes Systems on Infinite Sectors in Two Dimensions
- 2017
-
Ingår i: Integral equations and operator theory. - : Springer Science and Business Media LLC. - 0378-620X .- 1420-8989. ; 89:2, s. 151-207
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we establish sharp invertibility results for the elastostatics and hydrostatics single and double layer potential type operators acting on , , whenever is an infinite sector in . This analysis is relevant to the layer potential treatment of a variety of boundary value problems for the Lam, system of elastostatics and the Stokes system of hydrostatics in the class of curvilinear polygons in two dimensions, such as the Dirichlet, the Neumann, and the Regularity problems. Mellin transform techniques are used to identify the critical integrability indices for which invertibility of these layer potentials fails. Computer-aided proofs are produced to further study the monotonicity properties of these indices relative to parameters determined by the aperture of the sector and the differential operator in question.
|
|
