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A new definition of conditional invariance for boundary value problemsinvolving a wide range of boundary conditions (including initial value problemsas a special case) is proposed. It is shown that other definitions worked outin order to find Lie symmetries of boundary value problems with standardboundary conditions, follow as particular cases from our definition. Simpleexamples of direct applicability to the nonlinear problems arising inapplications are demonstrated. Moreover, the successful application of thedefinition for the Lie and conditional symmetry classification of a class of(1+2)-dimensional nonlinear boundary value problems governed by the nonlineardiffusion equation in a semi-infinite domain is realised. In particular, it isproved that there is a special exponent, $k=-2$, for the power diffusivity$u^k$ when the problem in question with non-vanishing flux on the boundaryadmits additional Lie symmetry operators compared to the case $k\not=-2$. Inorder to demonstrate the applicability of the symmetries derived, they are usedfor reducing the nonlinear problems with power diffusivity $u^k$ and a constantnon-zero flux on the boundary (such problems are common in applications anddescribing a wide range of phenomena) to (1+1)-dimensional problems. Thestructure and properties of the problems obtained are briefly analysed.Finally, some results demonstrating how Lie invariance of the boundary valueproblem in question depends on geometry of the domain are presented.

Lie and conditional symmetries of a class of nonlinear (1+2)-dimensional boundary value problems