Removability theorems for solutions of degenerate elliptic partial differential equations

Partial differential equations and quasiregular mappings

Quasilines and conformal mappings

Counterexamples for unique continuation

On the fusion problem for degenerate elliptic equations

Let F be a relatively closed subset of a Euclidean domain Ω. We investigate when solutions u to certain elliptic equations on Ω/F are restrictions of solutions on all of Ω. Specifically, we show that if ∂F is not too large, and u has a suitable decay rate near F, then u can be so extended.

Boundary Hölder Continuity and Quasiconformal Mappings