New Contributions to Hardy-type Inequalities and Boundary-Domain Integral Equations
| dc.contributor.advisor | Sorina Barza (Professor) | |
| dc.contributor.author | Bizuneh Minda | |
| dc.date.accessioned | 2025-08-17T21:15:07Z | |
| dc.date.available | 2025-08-17T21:15:07Z | |
| dc.date.issued | 2025-06 | |
| dc.description.abstract | For a large class of operators acting between weighted `1 spaces, exact formulas are obtained for their norms and the norms of their restrictions to the cones of nonnegative sequences and nonnegative monotone sequences. The weights involved are arbitrary nonnegative sequences and may differ in the domain and codomain spaces. The results are applied to the Ces`aro and Copson operators, giving their norms and their distances to the identity operator on the whole space and on the cones. Simplifications of these formulas are derived in the case of these operators acting on power-weighted `1. As an application, best constants are given for inequalities relating the weighted `1 norms of the Ces`aro and Copson operators both for general weights and for power weights. Moreover, we characterize the optimal non-absolute domain for the Hardy operator (and its dual) minus the identity, in the Lebesgue space Lp(0;1), 1 _ p _ 1. For variable coefficient Helmholtz equation, using appropriate parametrix, we formulate boundary-domain integral equations (BDIEs) for the Dirichlet and mixed (Dirichlet-Neumann) boundary value problems (BVPs) in a twodimensional bounded domain. The Dirichlet BVP is reduced to two different BDIE systems, depending on whether the trace or co-normal derivative of the third Green identity is employed on the boundary. On the other hand, the mixed BVP is reduced to four different BDIE systems, depending on whether the trace or co-normal derivative of the third Green identity is employed on the Dirichlet and Neumann boundaries. It is not clear in advance which of them will be more suitable for particular applications and for numerical implementation, and hence we analyzed all the BDIE systems. The equivalence between the BVPs and the formulated BDIE systems are shown. Fredholm properties, invertibility and unique solvability of BDIE systems are investigated in appropriate Sobolev spaces. | |
| dc.identifier.uri | https://etd.aau.edu.et/handle/123456789/6837 | |
| dc.language.iso | en_US | |
| dc.publisher | Addis Ababa University | |
| dc.subject | New Contributions | |
| dc.subject | Hardy-type Inequalities | |
| dc.subject | Boundary-Domain | |
| dc.subject | Integral Equations | |
| dc.title | New Contributions to Hardy-type Inequalities and Boundary-Domain Integral Equations | |
| dc.type | Thesis |