Plane-Like Minimal Surfaces in Periodic Media with Exclusions

I am indebted for many years of support and guidance, and also for leading me into the area of partial differential equations. Also, I am very grateful to Professor Rafael de la Llave for his encouragement and useful disscutions during my thesis work. I also express my gratitude to Professor Lawrence C. Evans for many interesting discussions, and for providing me with a great deal of insight towards the understanding of partial differential equations. Finally I would like to thank Professor William Beckner for his advice during the first stages of my studies and Professor Leszek Demkowicz for the use of the finite element codes 2Dhp90 and 3Dhp90.