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<p>In this paper, we obtain the one-dimensional symmetry and monotonicity of entire solutions for equations involving uniformly fractional parabolic operators via a sliding method. We adopt a generalized weighted average inequality and the maximum principle in unbounded domains, which are obtained by Chen and Wu in (Adv Nonlinear Stud 21:939–958, 2021), these methods are used to the uniformly fractional parabolic operators<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\displaystyle (-\triangle )^{s}_{a}(0&lt;s&lt;1)\)</EquationSource> </InlineEquation> in this paper. Then, using the sliding method, we derive the symmetry and monotonicity of entire solutions to uniformly fractional parabolic equations in the whole space.</p>

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Sliding method for uniformly fractional parabolic equations

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Pujun Yao

摘要

In this paper, we obtain the one-dimensional symmetry and monotonicity of entire solutions for equations involving uniformly fractional parabolic operators via a sliding method. We adopt a generalized weighted average inequality and the maximum principle in unbounded domains, which are obtained by Chen and Wu in (Adv Nonlinear Stud 21:939–958, 2021), these methods are used to the uniformly fractional parabolic operators \(\displaystyle (-\triangle )^{s}_{a}(0<s<1)\) in this paper. Then, using the sliding method, we derive the symmetry and monotonicity of entire solutions to uniformly fractional parabolic equations in the whole space.