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UBC Theses and Dissertations
On non-homogeneous quasi-linear PDEs involving the p-Laplacian and the critical sobolev exponent Yuan, Chaogui
Abstract
This thesis is devoted to the study of some quasi-linear PDEs involving the p-Laplacian. This type of problem represents a model case for the general quasi-linear elliptic equations. These problems arise from the Euler-Lagrange equations associated to various geometric problems and from topics like Non-Newtonian Fluids, Air Dynamics, Nonlinear Biological Population, Reaction-Diffusion Problems etc. The difficulties in- these problems come either from the lack of compactness of the approximate solutions or from the lack of symmetry in the corresponding energy functionals. The thesis has basically two parts. The first part is in Chapter 3, where we consider a problem related to Yamabe's prescribed curvature conjecture in Riemannian Geometry. This problem is critical in the sense that it involves the critical exponent in the Sobolev embedding. In particular, we show the existence of sign changing solutions by using the duality methods introduced by N. Ghoussoub. In the second part of the thesis, chapters 4 - 7, we consider the associated nonhomogeneous problems which arise from either a linear second member or from nonhomogeneous Dirichlet boundary conditions. Because of the lack of symmetry, the traditional equivariant variational principles do not apply here. To overcome those difficulties, we extend and use Bolle's method as well as Ekeland-Ghoussoub's virtual critical point theory to a Banach space setting.
Item Metadata
Title |
On non-homogeneous quasi-linear PDEs involving the p-Laplacian and the critical sobolev exponent
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1998
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Description |
This thesis is devoted to the study of some quasi-linear PDEs involving the p-Laplacian.
This type of problem represents a model case for the general quasi-linear elliptic equations.
These problems arise from the Euler-Lagrange equations associated to various
geometric problems and from topics like Non-Newtonian Fluids, Air Dynamics, Nonlinear
Biological Population, Reaction-Diffusion Problems etc. The difficulties in- these
problems come either from the lack of compactness of the approximate solutions or from
the lack of symmetry in the corresponding energy functionals.
The thesis has basically two parts. The first part is in Chapter 3, where we consider a
problem related to Yamabe's prescribed curvature conjecture in Riemannian Geometry.
This problem is critical in the sense that it involves the critical exponent in the Sobolev
embedding. In particular, we show the existence of sign changing solutions by using the
duality methods introduced by N. Ghoussoub.
In the second part of the thesis, chapters 4 - 7, we consider the associated nonhomogeneous
problems which arise from either a linear second member or from nonhomogeneous
Dirichlet boundary conditions. Because of the lack of symmetry, the traditional
equivariant variational principles do not apply here. To overcome those difficulties,
we extend and use Bolle's method as well as Ekeland-Ghoussoub's virtual critical point
theory to a Banach space setting.
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Extent |
4023762 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-06-02
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0079975
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1998-05
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.