Title

A study of degenerate elliptic partial differential equations

Date of Award

1998

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Advisor(s)

Tadeusz Iwaniec

Keywords

Degenerate, Elliptic, Partial differential, Partial differential equations

Subject Categories

Mathematics

Abstract

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 .

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