Originally presented as the author's thesis, Bonn. / Added t.p. with thesis statement inserted. Bibliography: p. 78-80.

Thesis (Ph. D.)--University of Michigan, 1975. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 71-73).

Thesis (doctoral)--Stockholms universitet. / Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

In this thesis, we study minimizers of the energy functional 𝐽 (𝑢,Ω) = ∫_Ω |∇𝑢|²/2 + 𝑊(𝑢) 𝑑𝑥 for two different potentials 𝑊(𝑢). In the first part we consider the Allen-Cahn energy, where 𝑊(𝑢) = (1 − 𝑢²)² is a doublewell potential which is relevant in the theory of phase transitions and minimal interfaces. We investigate the rigidity properties of global minimizers in low dimensions. In particular we extend a result of Savin on the De Giorgi’s conjecture to include minimizers that are not necessarily bounded, and that can have subquadratic growth at infinity. In the second part we consider potentials of the type 𝑊(𝑢) = 𝑢⁺ which appear in obstacletype free boundary problems. We establish higher order estimates and the analyticity of the regular part of the free boundary. Our method relies on developing higher order boundary Harnack estimates iteratively and deducing them from Schauder estimates for certain elliptic equations with degenerate weights. Finally we consider similar regularity questions of the free boundary in the Signorini problem which also known as the thin obstacle problem. We develop 𝐶²^𝛼 estimates of the free boundary under sharp assumptions on the coefficients and the data.

Yuen, Man Chun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 58-[60]). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

Typescript. / Thesis (Ph. D.)--University of Hawaii at Manoa, 1990. / Includes bibliographical references. / Microfiche. / vi, 96 leaves, bound ill. 29 cm

Thesis (Ph. D.)--Technische Universiteit Delft, 1989. / Summary also in Dutch. "Stellingen" (3 p.) inserted. Vita. Includes bibliographical references.

Thesis (Ph.D.)--Mississippi State University. Department of Mathematics and Statistics. / Title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--University of Alabama at Birmingham, 2008. / Title from PDF title page (viewed Sept. 23, 2009). Additional advisors: Inmaculada Aban, Alexander Frenkel, Wenzhang Huang, Yanni Zeng. Includes bibliographical references.