Second boundary value problem

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One of the boundary value problems (cf. Boundary value problem, partial differential equations) for partial differential equations. For example, let there be given a second-order elliptic equation


where , , in a bounded domain , with a normal at each point of the boundary . The second boundary value problem for equation (*) in is the following problem: Out of the set of all solutions of equation (*), isolate those solutions which have, at all boundary points, derivatives with respect to the interior normal and which satisfy the condition

where is a given function. The second boundary value problem is also known as the Neumann problem.


[1] A.V. Bitsadze, "Boundary value problems for second-order elliptic equations" , North-Holland (1968) (Translated from Russian)
[2] V.S. Vladimirov, "Equations of mathematical physics" , MIR (1984) (Translated from Russian)
[3] C. Miranda, "Partial differential equations of elliptic type" , Springer (1970) (Translated from Italian)
[4] I.G. Petrovskii, "Partial differential equations" , Saunders (1967) (Translated from Russian)



[a1] P.R. Garabedian, "Partial differential equations" , Wiley (1963)
[a2] R. Courant, D. Hilbert, "Methods of mathematical physics. Partial differential equations" , 2 , Interscience (1965) (Translated from German)
How to Cite This Entry:
Second boundary value problem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.K. Gushchin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article