Type of Document Dissertation Author Adimurthi, Karthik Author's Email Address firstname.lastname@example.org URN etd-04062016-020401 Title Global a priori Estimates and Sharp Existence Results for Quasilinear Equations on Nonsmooth Domains. Degree Doctor of Philosophy (Ph.D.) Department Mathematics Advisory Committee
Advisor Name Title Nguyen Cong Phuc Committee Chair Lipton, Robert Committee Co-Chair Almog, Yaniv Committee Member Dasbach, Oliver Committee Member Estrada, Ricardo Committee Member Chen, Jianhua Dean's Representative Keywords
- weighted estimates
- existence of weak solution
Date of Defense 2016-03-29 Availability unrestricted AbstractThis 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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