Boundary value problems for Laplace type operators

Wojciech Kozlowski. Lodz

Resumo:

Laplace type operators (also called weihted form Laplacians) are differential operators of the form $L=a d \delta + b \delta d$, where $a, b > 0$. These oerators appear in a natural way in differential geometry, e. g. the Laplace-Beltrami operator, or the Ahlfors operator.

We investigate four natural boundary value problems for these operators. We also show algebraic methods that can be applied to solve these operators in the space of differential forms in $\mathbb R^n$. These methods involve spherical harmonics, and some special $SO(n)$-invariant decomposition of the kernel of $L$.

© Wojciech Kozlowski.