Global a priori Estimates and Sharp Existence Results for Quasilinear Equations on Nonsmooth Domains.
This thesis deals obtaining global a priori estimates for quasilinear elliptic equations and sharp existence results for Quasilinear equations with gradient nonlinearity on the right. The main results are contained in Chapters 3, 4, 5 and 6. In Chapters 3 and 4, we obtain global unweighted a priori...
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| Format: | Others |
| Language: | en |
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LSU
2016
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| Online Access: | http://etd.lsu.edu/docs/available/etd-04062016-020401/ |
| Summary: | This thesis deals obtaining global a priori estimates for quasilinear elliptic equations and
sharp existence results for Quasilinear equations with gradient nonlinearity on the right.
The main results are contained in Chapters 3, 4, 5 and 6. In Chapters 3 and 4, we obtain
global unweighted a priori estimates for very weak solutions below the natural exponent and
weighted estimates at the natural exponent. The weights we consider are the well studied
Muckenhoupt weights. Using the results obtained in Chapter 4, we obtain sharp existence
result for quasilinear operators with gradient type nonlinearity on the right. We characterize
the function space which yields such sharp existence results. Finally in Chapter 6, we prove
existence of very weak solutions to quasilinear equations below the natural exponent with
measure data on the right.
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