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In this chapter we will prove some abstract results on the energy inequalities of strongly indefinite functionals on a Hilbert space E, whose norm and scalar product will be denoted, respectively, by \(\|\cdot \|\) and \(\left \langle \cdot ,\cdot \right \rangle \) . We anticipate that most of the results we will discuss could be carried out in a Banach spaces.

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Localized Energy Estimates for Strongly Indefinite Functionals

  • 章节

  • 发表日期：

    2025年

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  • Yanheng Ding,
  • Tian Xu

摘要

In this chapter we will prove some abstract results on the energy inequalities of strongly indefinite functionals on a Hilbert space E, whose norm and scalar product will be denoted, respectively, by \(\|\cdot \|\) and \(\left \langle \cdot ,\cdot \right \rangle \) . We anticipate that most of the results we will discuss could be carried out in a Banach spaces.