Regularity for quasilinear equations on degenerate singular sets

@article{Teixeira2012RegularityFQ,
  title={Regularity for quasilinear equations on degenerate singular sets},
  author={Eduardo V. Teixeira},
  journal={Mathematische Annalen},
  year={2012},
  volume={358},
  pages={241-256}
}
  • Eduardo V. Teixeira
  • Published 2012
  • Mathematics
  • Mathematische Annalen
  • We prove a new universal gradient continuity estimate for solutions to quasilinear equations with varying coefficients at singular set of degeneracy $$\fancyscript{S}(u) := \{X : D u(X) = 0 \}$$S(u):={X:Du(X)=0}. Our main Theorem reveals that along $$\fancyscript{S}(u)$$S(u), $$u$$u is asymptotically as regular as solutions to constant coefficient equations. In particular, along the critical set $$\fancyscript{S}(u)$$S(u), $$Du$$Du enjoys a modulus of continuity much superior than the, possibly… CONTINUE READING

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