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2 results

  • Existence of renormalized solutions to fully anisotropic and inhomogeneous elliptic problems

  • Part of
  • Bartosz Budnarowski, Ying Li
  • Journal:
    Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
    Published online by Cambridge University Press:
    31 October 2023, pp. 1-37
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  • We will present the proof of existence and uniqueness of renormalized solutions to a broad family of strongly non-linear elliptic equations with lower order terms and data of low integrability. The leading part of the operator satisfies general growth conditions settling the problem in the framework of fully anisotropic and inhomogeneous Musielak–Orlicz spaces. The setting considered in this paper generalized known results in the variable exponents, anisotropic polynomial, double phase and classical Orlicz setting.

  • Measure data elliptic problems with generalized Orlicz growth

  • Part of
  • Iwona Chlebicka
  • Journal:
    Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 153 / Issue 2 / April 2023
    Published online by Cambridge University Press:
    02 March 2022, pp. 588-618
    Print publication:
    April 2023
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      • Open access
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  • We study nonlinear measure data elliptic problems involving the operator of generalized Orlicz growth. Our framework embraces reflexive Orlicz spaces, as well as natural variants of variable exponent and double-phase spaces. Approximable and renormalized solutions are proven to exist and coincide for arbitrary measure datum and to be unique when for a class of data being diffuse with respect to a relevant nonstandard capacity. A capacitary characterization of diffuse measures is provided.