Corpus ID: 219259825

Wolff potentials and local behaviour of solutions to measure data elliptic problems with Orlicz growth

@article{Chlebicka2020WolffPA,
  title={Wolff potentials and local behaviour of solutions to measure data elliptic problems with Orlicz growth},
  author={I. Chlebicka and F. Giannetti and Anna Zatorska–Goldstein},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
  • I. Chlebicka, F. Giannetti, Anna Zatorska–Goldstein
  • Published 2020
  • Mathematics
  • arXiv: Analysis of PDEs
  • We establish pointwise estimates expressed in terms of a nonlinear potential of a generalized Wolff type for $A$-superharmonic functions with nonlinear operator $A:\Omega\times\mathbb{R}^n\to\mathbb{R}^n$ having measurable dependence on the spacial variable and Orlicz growth with respect to the last variable. The result is sharp as the same potential controls bounds from above and from below. Applying it we provide a bunch of precise regularity results including continuity and Holder continuity… CONTINUE READING
    4 Citations

    References

    SHOWING 1-10 OF 90 REFERENCES
    The Wolff potential estimate for solutions to elliptic equations with signed data
    • 4
    Fully anisotropic elliptic problems with minimally integrable data.
    • 13
    • PDF
    Wolff potential estimates for elliptic equations with nonstandard growth and applications
    • 24
    • Highly Influential
    • PDF
    Pointwise gradient estimates for a class of singular quasilinear equation with measure data
    • 11
    • PDF
    Nonlinear potentials, local solutions to elliptic equations and rearrangements
    • 21
    • PDF
    Gradient continuity estimates
    • 67
    Generalized superharmonic functions with strongly nonlinear operator
    • 3
    • PDF