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Zbl 0562.35001
Gilbarg, David; Trudinger, Neil S.
Elliptic partial differential equations of second order. 2nd ed. (English)
[B] 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${}\sp p$ 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.
[H.Jeggle]
MSC 2000:
*35-02 Research monographs (partial differential equations)
35J15 Second order elliptic equations, general
35J60 Nonlinear elliptic equations
35B50 Maximum principles (PDE)
35J25 Second order elliptic equations, boundary value problems
35J65 (Nonlinear) BVP for (non)linear elliptic equations
46E35 Sobolev spaces and generalizations
35B65 Smoothness of solutions of PDE
35B45 A priori estimates

Keywords: elliptic partial differential equations; second order; strong solutions; $L\sp p$ 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

Cited in: Zbl 1114.46030 Zbl 1042.35002 Zbl 0977.35150 Zbl 0963.60074 Zbl 0918.46033 Zbl 0884.35001 Zbl 0764.35039 Zbl 0691.35001 Zbl 0673.35023 Zbl 0721.35017 Zbl 0645.35006 Zbl 0639.35022 Zbl 0622.35022

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