Lectures on Partial Differential Equations
نویسنده
چکیده
A partial differential equation (PDE) of order m is a relation of the form F (x, u,Du,Du, · · · , Du) = 0. (0.1) Here F is a given function of x ∈ R, ”unknown” function u = u(x), and its derivatives up to order m. We denote Du the set of all the derivatives of u of order k. Using multi-indices l = (l1, · · · , ln), i.e. vectors in R with nonnegative integer components, we can write Du = { Du = D1 1 · · ·Dn n u = ∂u|l| ∂x1 1 · · · ∂xln n : |l| = l1 + · · ·+ ln = k } . (0.2)
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