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.

Committee Chair

Nguyen Cong Phuc

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