Localization Obstructions for Bubbling in High-Order Critical Elliptic Equations
Conditions that prevent a family of solutions to a high-order critical nonlinear equation (P_alpha u = Delta_g^k u + lower order = |u|^{2*-2-eps} u on a manifold) from concentrating into a single bubble. Students learn that whether such blow-up can occur is governed either by the mass of the Green's function of the operator or by how far the operator deviates from the conformally invariant GJMS operator, and that these obstructions are established through a sharp pointwise estimate on the solutions.
Localization of bubbling for high order nonlinear equations
We analyze the asymptotic pointwise behavior of families of solutions to the high-order critical equation $$P_αu_α=Δ_g^k u_α+\hbox{lot}=|u_α|^{2^\star-2-ε_α} u_α\hbox{ in }M$$ that behave like $$u_α=…