D. Kapanadze and B.-W. Schulze
abstract:
Crack problems are regarded as elements in a pseudo-differential
algebra, where the two sides $\intt S_\pm$ of the crack $S$ are
treated as interior boundaries and the boundary $Y$ of the crack as an edge
singularity. We employ the pseudo-differential calculus of boundary value
problems with the transmission property near $\intt S_\pm$ and the
edge pseudo-differential calculus (in a variant with Douglis-Nirenberg orders)
to construct parametrices of elliptic crack problems (with extra trace and
potential conditions along $Y$) and to characterise asymptotics of solutions
near $Y$ (expressed in the framework of continuous asymptotics). Our operator
algebra with boundary and edge symbols contains new weight and order
conventions that are necessary also for the more general calculus on manifolds
with boundary and edges.
Mathematics Subject Classification: 35S15, 35J70, 35J40, 38J40.
Key words and phrases: Crack theory, pseudo-differential boundary value problems, operator algebras on manifolds with singularities, conormal asym\-ptotics.