On the singular boundary value problem for elliptic equations
Kazunari Hayashida · Transactions of the American Mathematical Society · 1973
The operator L \mathcal {L} is elliptic and of second order in a domain Ω \Omega in R N {R^N} . We consider the following boundary value problem: L u = f \mathcal {L}u = f in Ω \Omega and B u = 0 \mathcal {B}u = 0 on ∂ Ω \partial \Omega , where B = a d / d n + β \mathcal {B} = ad/dn + \beta (d/dn is the conormal derivative on ∂ Ω \partial \Omega ). The coefficient α \alpha is assumed to be nonnegative. However, α \alpha may vanish partly on ∂ Ω \partial \Omega . Then the regularity of the weak solutions for the above problem is shown by the variational method.