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  3. 2 consider a partial differential equation for an unknown continuous...

Question: 2 consider a partial differential equation for an unknown continuous...

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2. Consider a partial differential equation for an unknown continuous function H(x, y) of (x,y) e R2o x R2o supplemented with boundary conditions H(z,0)-x(x), H(0,y)-φ(y), z,y 0, where X and φ are two given continuous functions satisfying χ(0-6(0). A) Show that if H solves (3), then it also solves an integral equation B) Show that there is at most one continuous function H(X,Y), X,Y 2 0 solving (5). Hint. Take two different solutions H and H, consider suposzyse H(x,y) - H(x, y)| for small є > 0 and use (5) to find a contradiction.

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