Hölder Continuity of Weak Solutions to Subelliptic Equations with Rough Coefficients.

Intro -- Contents -- Overview -- Chapter 1. Introduction -- 1. An extension of the Fefferman-Phong theorem to rough operators -- 2. Extensions of Hormander's theorem to rough operators -- 3. Applications to quasilinear equations -- Chapter 2. Comparisons of conditions -- 1. Flags and commutators -- 2. Homogeneous and prehomogeneous spaces -- 3. Comparability with the subunit balls -- Chapter 3. Proof of the general subellipticity theorem -- 1. W-weak solutions and admissible compositions -- 2. Weak reverse Hölder inequalities and Moser iteration -- 3. The strong Harnack inequality -- 4. Hölder continuity of solutions -- Chapter 4. Reduction of the proofs of the rough diagonal extensions of Hörmander's theorem -- 1. Accumulating sequences of Lipschitz cutoff functions in annuli -- 2. The axiom -- 3. The Sobolev and Poincaré inequalities -- 4. Adapted vector fields and prehomogeneous spaces -- 5. The reduction of the proofs -- Chapter 5. Homogeneous spaces and subrepresentation inequalities -- 1. The noninterference balls -- 2. The flag balls -- Chapter 6. Appendix -- 1. Necessity of the Fefferman-Phong condition -- 2. Necessity of the Sobolev and Poincaré inequalities -- 3. The noninterference balls A (x,r) and the reverse Hölder condition -- 4. Reverse Hölder examples -- 5. Product reverse Hölder -- 6. The noninterference conditions -- 7. Other notions of weak solution -- 8. Alternate methods of proof -- Bibliography -- Glossary of Terms and Symbols -- A -- B -- C -- D -- E -- F -- G -- H -- I -- L -- M -- N -- P -- Q -- R -- S -- T -- U -- V -- W.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.