Title: Bubbling on boundary submanifolds for the Lin–Ni–Takagi problem at higher critical exponents
Abstract: Let be a bounded domain in R n with smooth boundary ∂ .We consider the equationn-k-2 = 0 in , under zero Neumann boundary conditions, where d is a small positive parameter.We assume that there is a k-dimensional closed, embedded minimal submanifold K of ∂ which is nondegenerate, and a certain weighted average of sectional curvatures of ∂ is positive along K. Then we prove the existence of a sequence d = d j → 0 and a positive solution u d such thatin the sense of measures, where δ K stands for the Dirac measure supported on K and S is a positive constant.