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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.12637 |
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Table of Contents:
- The Grushin Laplacian $- Δ_α$ is a degenerate elliptic operator in $\mathbb{R}^{h+k}$ that degenerates on $\{0\} \times \mathbb{R}^k$. We consider weak solutions of $- Δ_αu= Vu$ in an open bounded connected domain $Ω$ with $V \in W^{1,σ}(Ω)$ and $σ> Q/2$, where $Q = h + (1+α)k$ is the so-called homogeneous dimension of $\mathbb{R}^{h+k}$. By means of an Almgren-type monotonicity formula we identify the exact asymptotic blow-up profile of solutions on degenerate points of $Ω$. As an application we derive strong unique continuation properties for solutions.