Global a priori Estimates and Sharp Existence Results for Quasilinear Equations on Nonsmooth Domains.

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.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2016

Author dc:creator

• Adimurthi, Karthik

• weighted estimates
• p-Laplacian
• existence of weak solution

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-04062016-020401
https://repository.lsu.edu/gradschool_dissertations/790

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-1789