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
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Recommended Citation
Almannaei, Abdulsalam Ahmeo, "A study of degenerate elliptic partial differential equations" (1998). Mathematics - Dissertations. 41.
https://surface.syr.edu/mat_etd/41
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