7 citations · 29 across the 17 of their papers we have counts for
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Strichartz estimates for Schrödinger equations with the multipole Aharonov--Bohm Hamiltonian
Mengxuan Yang, Junyong Zhang
We prove global-in-time Strichartz estimates for Schrödinger equations with multipole Aharonov--Bohm Hamiltonians on . As intermediate steps, we prove global-in-time…
Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces
Ziang Chen, Liqiang Huang, Mengxuan Yang +1
We establish a regularity theorem for second-order elliptic PDEs on in spectral Barron spaces. Under mild ellipticity and smallness assumptions, the solution gains…
From resolvent expansions at zero to long time wave expansions
T. J. Christiansen, K. Datchev, M. Yang
We prove a general abstract theorem deducing wave expansions as time goes to infinity from resolvent expansions as energy goes to zero, under an assumption of polynomial boundednes…
Low energy resolvent asymptotics of the multipole Aharonov--Bohm Hamiltonian
T. J. Christiansen, K. Datchev, M. Yang
We compute low energy asymptotics for the resolvent of the Aharonov--Bohm Hamiltonian with multiple poles for both integer and non-integer total fluxes. For integral total flux we…
Resolvent estimates for the magnetic Hamiltonian with singular vector potentials and applications
Mengxuan Yang
For the magnetic Hamiltonian with singular vector potentials, we analytically continue the resolvent to a logarithmic neighborhood of the positive real axis and prove resolvent est…
The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials
Mengxuan Yang
We study leading order singularities of the wave trace of the Aharonov--Bohm Hamiltonian on with multiple solenoids under a generic assumption that no three solenoid…
New counterexamples to Strichartz estimates for the wave equation on a 2d model convex domain
Oana Ivanovici, Gilles Lebeau, Fabrice Planchon
We prove that the range of Strichartz estimates on a model 2D convex domain may be further restricted compared to the known counterexamples due to the first author. Our new family…
Propagation of polyhomogeneity, Diffraction and Scattering on Product Cones
Mengxuan Yang
We consider diffraction of waves on a product cone. We first show that diffractive waves enjoy a one-step polyhomogeneous asymptotic expansion, which is an improvement of Cheeger-T…
Scattering resonances on truncated cones
Dean Baskin, Mengxuan Yang
We consider the problem of finding the resonances of the Laplacian on truncated Riemannian cones. In a similar fashion to Cheeger--Taylor, we construct the resolvent and scattering…