There are three types of boundary conditions commonly encountered in the solution of partial differential equations:
1. Dirichlet boundary conditions specify the value of the function on a surface 
.
2. Neumann boundary conditions specify the normal derivative of the function on a surface,
3. Robin boundary conditions. For an elliptic partial differential equation in a region 
, Robin boundary conditions specify the sum of 
and the normal derivative of 
at all points of the boundary of 
, with 
and 
being prescribed.
See also
Boundary Value Problem, Cauchy Conditions, Dirichlet Boundary Conditions, Goursat Problem, Initial Conditions, Initial Value Problem, Neumann Boundary Conditions, Partial Differential Equation, Robin Boundary Conditions
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References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 502-504, 1985.Morse, P. M. and Feshbach, H. "Boundary Conditions and Eigenfunctions." Ch. 6 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 495-498 and 676-790, 1953.
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Cite this as:
Weisstein, Eric W. "Boundary Conditions." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BoundaryConditions.html