A theorem on global regularity of solutions of a singular elliptic equation

Abstract

Let u be a solution of a singular elliptic equation Δu + bu_r + f ≡ 0 where b has a first order singularity on the outer boundary ∂₊ of an annular domain, and assume that u and ∞ satisfy certain decay conditions near ∂₊. Then a regularity property of u near ∂₊ is proved, provided the residue of b at ∂₊ is large enough

Keywords:

• Elliptic equations of degenerate type
• regularity of generalized solutions
• smoothness of solutions

AMS(MOS)::

• 35J70
• 35D10
• 35B65