Existence and regularity for a p-Laplacian problem in ℝN with singular, convective, and critical reaction

Abstract

We prove an existence result for a p-Laplacian problem set in the whole Euclidean space and exhibiting a critical term perturbed by a singular, convective reaction. The approach used combines variational methods, truncation techniques, and concentration compactness arguments, together with set-valued analysis and fixed point theory. De Giorgi’s technique, a priori gradient estimates, and nonlinear regularity theory are employed to obtain local C1,α regularity of solutions, as well as their pointwise decay at infinity. The result is new even in the non-singular case, also for the Laplacian.