#### 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 .

#### Access

Surface provides description only. Full text is available to ProQuest subscribers. Ask your Librarian for assistance.

#### Recommended Citation

Almannaei, Abdulsalam Ahmeo, "A study of degenerate elliptic partial differential equations" (1998). *Mathematics - Dissertations.* Paper 41.

http://surface.syr.edu/mat_etd/41

http://libezproxy.syr.edu/login?url=http://proquest.umi.com/pqdweb?did=733076391&sid=2&Fmt=2&clientId=3739&RQT=309&VName=PQD