A Hopf-type boundary point lemma for pairs of solutions to quasilinear equations

Abstract

We show a Hopf boundary point lemma for $u=u_1-u_2,$ given $u_1,u_2\in C^{1,\alpha }$ each weak solutions to a quasilinear equation ${\sum }_{i=1}^n{D}_i(A^i(x,u,Du))+B(x,u,Du)=0$ under mild boundedness assumptions on $A^1,\dots ,A^n,B.$

19 pages