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We prove that operators of the form \(A=-a(x)^2\varDelta ^{2}\) , with suitable growth conditions on the coefficient a(x), generate analytic semigroups in \(L^1(\mathbb {R}^N)\) . In particular, we deduce generation results for the operator \(A :=- (1+|x|^2)^{\alpha } \varDelta ^{2}\) , \(0\le \alpha \le 2\) . Moreover, we characterize the maximal domain of A in \(L^1(\mathbb {R}^N)\) .

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Fourth-Order Operators with Unbounded Coefficients in \(L^1\) Spaces

  • 会议论文

  • 发表日期：

    2026年

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  • Federica Gregorio,
  • Chiara Spina,
  • Cristian Tacelli

摘要

We prove that operators of the form \(A=-a(x)^2\varDelta ^{2}\) , with suitable growth conditions on the coefficient a(x), generate analytic semigroups in \(L^1(\mathbb {R}^N)\) . In particular, we deduce generation results for the operator \(A :=- (1+|x|^2)^{\alpha } \varDelta ^{2}\) , \(0\le \alpha \le 2\) . Moreover, we characterize the maximal domain of A in \(L^1(\mathbb {R}^N)\) .