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.
| Identifer | oai:union.ndltd.org:LSU/oai:etd.lsu.edu:etd-04062016-020401 |
| Date | 04 May 2016 |
| Creators | Adimurthi, Karthik |
| Contributors | Dasbach, Oliver, Estrada, Ricardo, Chen, Jianhua, Almog, Yaniv, Lipton, Robert, Nguyen Cong Phuc |
| Publisher | LSU |
| Source Sets | Louisiana State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lsu.edu/docs/available/etd-04062016-020401/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached herein a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to LSU or its agents the non-exclusive license to archive and make accessible, under the conditions specified below and in appropriate University policies, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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