Summary
In this paper we characterize the sets of weighted capacity zero and the weighted null sets, and state analogous properties for the correspondent unweighted sets. Then we provide removable singularity results for weak solutions of degenerate quasilinear parabolic equations and their elliptic equivalents supposing that the singular set is one of the above types of sets. In obtaining these results the basic idea is to connect the capacity (or the nullity indices) of the singular set to the Lebesgue classes of the weight μ, of 1/μ, and of the xi-derivatives. of the weak solution.
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Saraiva, L.M.R. Removable singularities of solutions of degenerate quasilinear equations. Annali di Matematica pura ed applicata 141, 187–221 (1985). https://doi.org/10.1007/BF01763174
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DOI: https://doi.org/10.1007/BF01763174