Acknowledgements

There are many people that have earned my gratitude for their contribution to my time in graduate school. I owe my deepest gratitude to my adivisor Vladimı́r Šverák for his supervision, encouragement, and support. It would have been impossible to write this thesis without his constant help and guidance. I have learned from him innumerable lessons and insights on all aspects of the workings of academic research. Special thanks goes to Professor Poláčik, who has been very supportive and helped numerously in all stages of my graduate study. I also take this chance to thank Professor Escauriaza for helpful advices on the project in the first half of this thesis, for many inspiring discussions during my visit to UPV/EHU in beautiful Bilbao. This work is partially supported by Doctoral Dissertation Fellowship of Univer-sity of Minnesota. Some of the work appearing in this thesis was carried out when i I was under the support of Louis Dosdall Fellowship of University of Minnesota