In this paper, we study the singular elliptic equation Lu + K(x)up = 0. where L is a uniformly elliptic operator of divergence form, p > 1 and K(x) has a singularity at the origin. We prove that this equation does not possess any positive (local) solution in any punctured neighborhood of the origin if there exist two constants C1, C2 such that C1 |x|σ ≥ K(x) ≥ C2 | x |σ near the origin for some σ ≥ -2 (with no other condition on the gradient of K). In fact, an integral condition is derived.
|Original language||English (US)|
|Number of pages||3|
|Journal||Proceedings of the American Mathematical Society|
|State||Published - Aug 1983|
- Singular elliptic equation