A study of degenerate elliptic partial differential equations
Abdulsalam Ahmeo Almannaei · Syracuse University Libraries (Syracuse University) · 1998
In this thesis, two types of second order elliptic partial differential equations will be studied. The first type is the following equation [Special characters omitted.] for a function u of Sobolev class [Special characters omitted.] Here A, B and C are measurable functions on Ω with A > 0, C > 0 and AC - B ² > 0 a.e . Our main result will be that u is of class C 1 (Ω) provided that [Special characters omitted.] is locally integrable on Ω. The second equation we will study is the non-homogeneous p -harmonic equation [Special characters omitted.] for a function [Special characters omitted.] where [Special characters omitted.] with [Special characters omitted.] Our main result is the following: THEOREM. Let u be a non-homogeneous p -harmonic function on [Special characters omitted.] of class [Special characters omitted.] where 1 < p ≤ 2. If [Special characters omitted.] then [Special characters omitted.] and the following uniform estimate holds [Special characters omitted.] Among other applications, this theorem will be used to establish higher integrability of ∇ u .