Construction of analytical solutions

To construct this projection, we introduce the function a G P (f2y)nC°°(f2y) by the formula 

Taking into account (2.179), we have to prove that 

By the above properties of x°, (x°) oiie can easily verify that the constructed function x = (IR, w) justifies the following boundary value problem  

Then x is the solution of the variational inequality (2.174) with the right-hand side / = (—WxxyU xxxx)- For instance, this holds provided that u G 77(fly) n (772(fly) X 774(fly)). 

We give some examples of exact solutions for given /. 

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