On the critical point regularity for quasilinear problems

Prof. Eduardo Teixeira

Abstract:The C^p' regularity conjecture claims that any solution to −∆_p = f(x), with f bounded and p>2, is locally of class C^p' = C^1,1/(p-1). That the sharp estimate is attained by a naive looking, radially symmetric example whose p-laplacian is actually constant, begs the question: assuming the C^p' regularity conjecture true, is there any further regularity left for non-homogeneous problems driven by the p-laplacian? In this talk I shall discuss this question through a new prism.