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New solutions to local and non-local elliptic equations Chan, Hon To Hardy
Abstract
We obtain a few existence results for elliptic equations. We develop in Chapter 2 a new infinite dimensional gluing scheme for fractional elliptic equations in the mildly non-local setting. Here it is applied to the catenoid. As a consequence of this method, a counter-example to a fractional analogue of De Giorgi conjecture can be obtained [51]. Then, in Chapter 3, we construct singular solutions to the fractional Yamabe problem using conformal geometry. Fractional order ordinary differential equations are studied. Finally, in Chapter 4, we obtain the existence to a suitably perturbed doublycritical Hardy–Schr¨odinger equation in a bounded domain in the hyperbolic space.
Item Metadata
| Title |
New solutions to local and non-local elliptic equations
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2018
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| Description |
We obtain a few existence results for elliptic equations.
We develop in Chapter 2 a new infinite dimensional gluing scheme for fractional
elliptic equations in the mildly non-local setting. Here it is applied to the catenoid. As a consequence of this method, a counter-example to a fractional analogue of De Giorgi conjecture can be obtained [51].
Then, in Chapter 3, we construct singular solutions to the fractional Yamabe problem using conformal geometry. Fractional order ordinary differential equations are studied.
Finally, in Chapter 4, we obtain the existence to a suitably perturbed doublycritical Hardy–Schr¨odinger equation in a bounded domain in the hyperbolic space.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2018-07-03
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0368784
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2018-09
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International