Find bounded function that solves the problem - the

Question

Let p:={(x,y) in R^2: x^2 +y^2<1}

Find bounded function u(x,y) that solves the following problem:

0=Ux,x +Ut,t, for (x,y) in p

u(x,y)= g(x,y) for (x,y) in p with g(x,y):=2 x^2 + y^2.

the solution cannot contain unevaluated infinite sums and unevaluated integrals.

the solution should be given in Cartesian coordinates