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<p>In the present paper we study a second order abstract differential equation of elliptic type with nonlocal boundary conditions in the framework of Hö lderian spaces. We give necessary and sufficient conditions on the data to obtain some results about existence, uniqueness and regularity of a semiclassical, semistrict and strict solution. Our techniques are based on the semigroup theory, the fractional powers of linear operators and some properties of real interpolation spaces.</p>

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Study of general elliptic problems with nonlocal boundary conditions in the Hölderian framework

  • 期刊论文

  • 发表日期：

    2025年12月13日

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  • Hamdi Brahim,
  • Menad Abdallah,
  • Nouara Ahmad

摘要

In the present paper we study a second order abstract differential equation of elliptic type with nonlocal boundary conditions in the framework of Hö lderian spaces. We give necessary and sufficient conditions on the data to obtain some results about existence, uniqueness and regularity of a semiclassical, semistrict and strict solution. Our techniques are based on the semigroup theory, the fractional powers of linear operators and some properties of real interpolation spaces.