Fourth-order operators with unbounded coefficients in $L^1$ spaces

Federica Gregorio; Chiara Spina; Cristian Tacelli

Fourth-order operators with unbounded coefficients in $L^1$ spaces

Functional Analysis 2025-10-21 v2

Authors: Federica Gregorio , Chiara Spina , Cristian Tacelli

Abstract

We prove that operators of the form $A=-a(x)^2\Delta^{2}$ , 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 $A :=- (1+|x|^2)^{\alpha} \Delta^{2}$ , $0\leq\alpha\leq2$ . Moreover, we characterise the maximal domain of $A$ in $L^1(\mathbb{R}^N)$ .

Keywords

operator semigroups operator theory maximal operators

Cite

@article{arxiv.2407.10551,
  title  = {Fourth-order operators with unbounded coefficients in $L^1$ spaces},
  author = {Federica Gregorio and Chiara Spina and Cristian Tacelli},
  journal= {arXiv preprint arXiv:2407.10551},
  year   = {2025}
}

Comments

arXiv admin note: text overlap with arXiv:2401.14187

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