Question: Give a direct proof that if U is bounded and u C(UT) n C(T) solves the heat equation, then max u = max u.

Give a direct proof that if U is bounded and u C(UT) n C(T) solves the heat equation, then max u = max u. T

Give a direct proof that if U is bounded and u C(UT) n C(T) solves the heat equation, then max u = max u. T (Hint: Define ue=u-et for e > 0, and show u cannot attain its maximum over T at a point in UT.)

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