$L^p$-regularity for fourth-order Schrödinger operators with unbounded or degenerate coefficients
Year: 2026
Type: preprint
Abstract: We prove that operators of the form $A=-Δ^{2}-V(x)$, with $|D V(x)|\leq γV(x)^\frac{5}{4}+ C_γ$ for some $γ$ small enough and $C_γ$ positive constant, generate analytic semigroups in $L^p(\mathbb{R}^N)$ for $1\leq p<\infty$ and in $C_0(\mathbb{R}^N)$. Moreover, we characterize the maximal domain of such operators.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223064413