Abstract
where DXj denotes partial differentiation with respect to Xj. The sum in (1) is taken over all vectors i with O^iy^my, where m i s a fixed vector with positive integer components. For the domain of the functional L it is convenient to take the class of all functions v of class C and having support compact on G (i.e., compact and contained in G). Then L(v) is well defined when the coefficients Ai axe all locally integrable in G. Also the following notations are meaningful (with exceptional sets of measure zero) for a locally integrable function ƒ :
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