Elliptic partial differential equations of second order. 2nd ed. (English) Zbl 0562.35001

Gilbarg, David; Trudinger, Neil S.

Grundlehren der Mathematischen Wissenschaften, 224. Berlin etc.: Springer-Verlag. XIII, 513 p. DM 128.00; $ 47.80 (1983).

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, Hölder estimates for the first derivatives, extension and interpolation of Sobolev spaces, the eigenvalue problem.

Reviewer: H.Jeggle

MSC:

35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations
35J15	Second-order elliptic equations
35J60	Nonlinear elliptic equations
35B50	Maximum principles in context of PDEs
35J25	Boundary value problems for second-order elliptic equations
35J65	Nonlinear boundary value problems for linear elliptic equations
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35B65	Smoothness and regularity of solutions to PDEs
35B45	A priori estimates in context of PDEs

Keywords:

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; Hölder estimates; interpolation of Sobolev spaces; eigenvalue problem

Citations:

Zbl 0361.35003