engleski

Singular dimension of solution set of some classes of elliptic equations

We show that a class of elliptic equations involving the Laplace operator on the left-hand side, with zero boundary data on a bounded open domain of R^N, such that the right-hand sides are in L^2, has singular dimension of solution set is equal to N-4. The singular dimension is defined as the supremum of Hausdorff dimension of singular sets of weak solutions generated by right-hand sides. A result is presented involving p-Laplace operators with right-hand sides in L^{;p'};: for p>2 the singular dimension of solution set is N-pp'.

elliptic equation; singular set; Hausdorff dimension; singular dimension

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