For a class of degenerate pseudodifferential operators, local parametrices are constructed. This is done in the framework of a pseudodifferential calculus upon adding conditions of trace and potential type, respectively, along the boundary on which the operators degenerate.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc60-0-13, author = {Ingo Witt}, title = {A calculus for a class of finitely degenerate pseudodifferential operators}, journal = {Banach Center Publications}, volume = {60}, year = {2003}, pages = {161-189}, zbl = {1071.35131}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc60-0-13} }
Ingo Witt. A calculus for a class of finitely degenerate pseudodifferential operators. Banach Center Publications, Tome 60 (2003) pp. 161-189. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc60-0-13/