Title page for ETD etd-04062016-020401

Type of Document Dissertation
Author Adimurthi, Karthik
Author's Email Address karthikaditi@gmail.com
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
  • weighted estimates
  • p-Laplacian
  • existence of weak solution
Date of Defense 2016-03-29
Availability unrestricted
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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