Regularity of Fourth and Second Order Nonlinear Elliptic Equations

dc.contributor.advisor	Warren, Micah
dc.contributor.author	Bhattacharya, Arunima
dc.date.accessioned	2019-09-18T19:16:19Z
dc.date.available	2019-09-18T19:16:19Z
dc.date.issued	2019-09-18
dc.description.abstract	In this thesis, we prove regularity theory for nonlinear fourth order and second order elliptic equations. First, we show that for a certain class of fourth order equations in the double divergence form, where the nonlinearity is in the Hessian, solutions that are $C^{2,\alpha}$ enjoy interior estimates on all derivatives. Next, we consider the fourth order Lagrangian Hamiltonian stationary equation for all phases in dimension two and show that solutions, which are $C^{1,1}$ will be smooth and we also derive a $C^{2,\alpha}$ estimate for it. We also prove explicit $C^{2,\alpha}$ interior estimates for viscosity solutions of fully nonlinear, uniformly elliptic second order equations, which are close to linear equations and we compute an explicit bound for the closeness.	en_US
dc.identifier.uri	https://hdl.handle.net/1794/24840
dc.language.iso	en_US
dc.publisher	University of Oregon
dc.rights	All Rights Reserved.
dc.title	Regularity of Fourth and Second Order Nonlinear Elliptic Equations
dc.type	Electronic Thesis or Dissertation
thesis.degree.discipline	Department of Mathematics
thesis.degree.grantor	University of Oregon
thesis.degree.level	doctoral
thesis.degree.name	Ph.D.

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