Second Order Elliptic Equations and Elliptic SystemsThere are two parts to the book. In the first part, a complete introduction of various kinds of a priori estimate methods for the Dirichlet problem of second order elliptic partial differential equations is presented. In the second part, the existence and regularity theories of the Dirichlet problem for linear and nonlinear second order elliptic partial differential systems are introduced. The book features appropriate materials and is an excellent textbook for graduate students. The volume is also useful as a reference source for undergraduate mathematics majors, graduate students, professors, and scientists. |
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Contents
| 3 | |
Schauder Theory | 17 |
Lp Theory | 37 |
De GiorgiNashMoser Estimates | 53 |
Quasilinear Equations of Divergence Form | 67 |
KrylovSafonov Estimates | 79 |
Fully Nonlinear Elliptic Equations | 99 |
20 | 111 |
Further regularity and counterexamples | 178 |
27 | 180 |
The reverse Hélder inequality and Lp estimates for | 198 |
33 | 201 |
assess | 204 |
Sobolev Spaces | 209 |
Sards Theorem | 215 |
Proof of the Reverse Hfiilder Inequality | 225 |
Other editions - View all
Second Order Elliptic Equations and Elliptic Systems Ya-Zhe Chen,Lan-Cheng Wu No preview available - 1998 |
Second Order Elliptic Equations and Elliptic Systems Yazhe Chen,Lancheng Wu No preview available - 1998 |
Common terms and phrases
Applying Lemma assume without loss ball Banach space boundary bounded domain bounded linear operator choose converges cubes cutoff function deduce defined Definition 1.3 denote depends Dirichlet problem divergence form elliptic equations Euler system exists find finite first follows Fréchet derivative G Q0 growth condition Harnack inequality Holder estimates Ifu G implies Lebesgue Let Q Let the assumptions Linear Elliptic Systems Math maximum principle method modulus of continuity mollified Morrey natural structure conditions nonlinear elliptic systems nonnegative norm obtain open set Poincaré’s inequality positive constants priori estimate proof is complete prove Q satisfies regularity of weak satisfies satisfy Schauder theory second order elliptic Sobolev embedding theorem Sobolev space solution of 1.1 solution u G structure conditions F1 subset sufficiently Suppose Systems of Divergence Theorem 2.1 valid weak derivatives weak solution x0 G Q
Bibliographic information
| Title | Second Order Elliptic Equations and Elliptic Systems Volume 174 of Translations of mathematical monographs, ISSN 0065-9282 |
| Authors | Ya-Zhe Chen, Lan-Cheng Wu |
| Edition | revised |
| Publisher | American Mathematical Soc., 1998 |
| ISBN | 0821819240, 9780821819241 |
| Length | 246 pages |
| Subjects | › Mathematics / Reference |
| Export Citation | BiBTeX EndNote RefMan |