Zobrazeno 1 - 10
of 181
pro vyhledávání: '"Banerjee, Agnid"'
Autor:
Banerjee, Agnid, Garofalo, Nicola
We prove a theorem of unique continuation in measure for nonlocal equations of the type $(\partial_t - \Delta)^s u= V(x,t) u$, for $0
Externí odkaz:
http://arxiv.org/abs/2412.03536
We establish a new sharp estimate of the order of vanishing of solutions to parabolic equations with variable coefficients. For real-analytic leading coefficients, we prove a localised estimate of the nodal set, at a given time-level, that generalise
Externí odkaz:
http://arxiv.org/abs/2405.13253
Autor:
Banerjee, Agnid, Garofalo, Nicola
We establish an optimal asymptotic on rings for a subelliptic Helmholtz equation with mixed homogeneities.
Externí odkaz:
http://arxiv.org/abs/2311.11559
Autor:
Banerjee, Agnid, Garofalo, Nicola
In his seminal 1943 paper F. Rellich proved that, in the complement of a cavity $\Omega = \{x\in \mathbb R^n\mid |x|>R_0\}$, there exist no nontrivial solution $f$ of the Helmholtz equation $\Delta f = - \lambda f$, when $\lambda>0$, such that $\int_
Externí odkaz:
http://arxiv.org/abs/2311.05905
Autor:
Banerjee, Agnid, Ghosh, Abhishek
For $s \in [1/2, 1)$, let $u$ solve $(\partial_t - \Delta)^s u = Vu$ in $\mathbb R^{n} \times [-T, 0]$ for some $T>0$ where $||V||_{ C^2(\mathbb R^n \times [-T, 0])} < \infty$. We show that if for some $0< c< T$ and $\epsilon>0$ $$\frac{1}{c} \int_{[
Externí odkaz:
http://arxiv.org/abs/2307.10887
Autor:
Banerjee, Agnid, Ghosh, Abhishek
We show that if $u$ solves the fractional parabolic equation $(\partial_t - \Delta )^s u = Vu$ in $B_5 \times (-25, 0]$ ($0
Externí odkaz:
http://arxiv.org/abs/2306.00341
Autor:
Banerjee, Agnid, Garofalo, Nicola
In this short note we prove that if $u$ solves $(\partial_t - \Delta)^s u = Vu$ in $\mathbb R^n_x \times \mathbb R_t$, and vanishes to infinite order at a point $(x_0, t_0)$, then $u \equiv 0$ in $\mathbb R^n_x \times \mathbb R_t$. This sharpens (and
Externí odkaz:
http://arxiv.org/abs/2301.12239
In this paper, we prove gradient continuity estimates for viscosity solutions to $\Delta_{p}^N u- u_t= f$ in terms of the scaling critical $L(n+2,1 )$ norm of $f$, where $\Delta_{p}^N$ is the game theoretic normalized $p-$Laplacian operator defined i
Externí odkaz:
http://arxiv.org/abs/2211.15246
In his seminal 1981 study D. Jerison showed the remarkable negative phenomenon that there exist, in general, no Schauder estimates near the characteristic boundary in the Heisenberg group $\mathbb H^n$. On the positive side, by adapting tools from Fo
Externí odkaz:
http://arxiv.org/abs/2210.12950
Autor:
Banerjee, Agnid, Senapati, Soumen
In this paper, we introduce and analyse an explicit formulation of fractional powers of the parabolic Lam\'e operator $\mathbb{H}$ and we then study the extension problem associated to such non-local operators. We also study the various regularity pr
Externí odkaz:
http://arxiv.org/abs/2208.11598