Identifier
etd-04062016-020401
Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
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.
Date
2016
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Recommended Citation
Adimurthi, Karthik, "Global a priori Estimates and Sharp Existence Results for Quasilinear Equations on Nonsmooth Domains." (2016). LSU Doctoral Dissertations. 790.
https://repository.lsu.edu/gradschool_dissertations/790
Committee Chair
Nguyen Cong Phuc
DOI
10.31390/gradschool_dissertations.790