Date of Award
2013
Publisher
North Dakota State University
Document Type
Dissertation
Degree Awarded
Doctor of Philosophy (PhD)
Program
Mathematics
Department
Mathematics
College
Science and Mathematics
Faculty Advisor
Akhmedov, Azer
Description
In the first part of the thesis the effective yield set of ionic polycrystals is characterized by means of variational principles in L∞ that are associated to supremal functionals acting on matrix-valued divergence-free fields. The second part of the thesis is concerned with the study of the asymptotic behavior, as p → ∞, of the first and second eigenvalues and the corresponding eigenfunctions for the p(x)-Laplacian with Robin and Neumann boundary conditions, in an open, bounded domain with smooth boundary. We obtain uniform bounds for the sequences of eigenvalues (suitably rescaled), and we prove that the positive eigenfunctions converge uniformly to viscosity solutions of problems involving the ∞-Laplacian subject to appropriate boundary conditions.
Recommended Citation
Abdullayev, Farhod, "Variational Methods for Polycrystal Plasticity and Related Topics in Partial Differential Equations" (2013). Mathematics. 23.
https://digitalcommons.ndsu.edu/mathematics/23
Rights
NDSU Policy 190.6.2
Rights Link
https://www.ndsu.edu/fileadmin/policy/190.pdf
Handle Identifier
https://hdl.handle.net/10365/27089