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In this chapter we present various results that are included in the “basic tool kit of viscosity solution techniques” in Cirant et al. (Comparison principles by monotonicity and duality for constant coefficient nonlinear potential theory and PDEs, vol. 218, 2023): the Bad Test Jet Lemma 7.1, the Definitional Comparison Lemma 7.3, and Proposition 7.5 which gathers various widely used constructions of \({\mathcal F}\) -subharmonic functions obtained by algebraic operations, optimization procedures and limits.

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Basic Tools in Nonlinear Potential Theory

  • 章节

  • 发表日期：

    2025年

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  • Kevin R. Payne,
  • Davide Francesco Redaelli

摘要

In this chapter we present various results that are included in the “basic tool kit of viscosity solution techniques” in Cirant et al. (Comparison principles by monotonicity and duality for constant coefficient nonlinear potential theory and PDEs, vol. 218, 2023): the Bad Test Jet Lemma 7.1, the Definitional Comparison Lemma 7.3, and Proposition 7.5 which gathers various widely used constructions of \({\mathcal F}\) -subharmonic functions obtained by algebraic operations, optimization procedures and limits.