an:03895476
Zbl 0562.35001
Gilbarg, David; Trudinger, Neil S.
Elliptic partial differential equations of second order. 2nd ed
EN
Grundlehren der Mathematischen Wissenschaften, 224. Berlin etc.: Springer-Verlag. XIII, 513 p. DM 128.00; {\$} 47.80 (1983).
00419483
1983
b
35-02 35J15 35J60 35B50 35J25 35J65 46E35 35B65 35B45
elliptic partial differential equations; second order; strong solutions; \(L^ p\) theory; maximum principles; local properties; fully nonlinear equations; comparison principles; continuation method; interior estimates; second derivatives; capacity; H??lder estimates; interpolation of Sobolev spaces; eigenvalue problem
In the second edition of this esteemed and useful exposition the authors made some minor revisions and added some material concerning recent developments of the theory. There are two additional chapters dealing with strong solutions of linear equations (L\({}^ p\) theory, maximum principles and local properties of strong solutions) and the classical Dirichlet problem for fully nonlinear equations (Maximum and comparison principles, continuation method, interior estimates for second derivatives), respectively. Other chapters are supplemented by sections concerning capacity, H??lder estimates for the first derivatives, extension and interpolation of Sobolev spaces, the eigenvalue problem.
H.Jeggle
Zbl 0361.35003