Zobrazeno 1 - 10
of 19
pro vyhledávání: '"Longjuan Xu"'
Publikováno v:
SIAM Journal on Mathematical Analysis. 54:3609-3635
We study stationary Stokes systems in divergence form with piecewise Dini mean oscillation coefficients and data in a bounded domain containing a finite number of subdomains with $C^{1,\rm{Dini}}$ boundaries. We prove that if $(u, p)$ is a weak solut
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1895a5c1117f755c041533679be87500
https://doi.org/10.1137/21m1423518
https://doi.org/10.1137/21m1423518
Publikováno v:
Quarterly of Applied Mathematics. 80:607-639
We establish boundary gradient estimates for both Lamé systems with partially infinite coefficients and perfect conductivity problem. The inclusion and the matrix domain are both assumed to be of C 1 , α C^{1, \alpha } , weaker than C 2 , α C^{2,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8e1c81326dd815b6e05bdfce17383ad0
https://doi.org/10.1090/qam/1621
https://doi.org/10.1090/qam/1621
Publikováno v:
Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 38:953-979
In high-contrast composite materials, the electric field concentration is a common phenomenon when two inclusions are close to touch. It is important from an engineering point of view to study the dependence of the electric field on the distance betw
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d537d0f63ce0ee173fee491a894a1f9c
https://doi.org/10.1016/j.anihpc.2020.09.009
https://doi.org/10.1016/j.anihpc.2020.09.009
Publikováno v:
SIAM Journal on Mathematical Analysis; 2023, Vol. 55 Issue 5, p4493-4536, 44p
Autor:
Longjuan Xu, Hongjie Dong
Publikováno v:
Potential Analysis. 54:409-449
In this paper, we prove that any $W^{2,1}$ strong solution to second-order non-divergence form elliptic equations is locally $W^{2,\infty}$ and piecewise $C^{2}$ when the leading coefficients and data are of piecewise Dini mean oscillation and the lo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a015f7a7dcc3c348aa48665dffa20874
https://doi.org/10.1007/s11118-020-09832-w
https://doi.org/10.1007/s11118-020-09832-w
Publikováno v:
Journal of Differential Equations. 267:6644-6690
In composite materials, the inclusions are frequently spaced very closely. The electric field concentrated in the narrow regions between two adjacent perfectly conducting inclusions will always become arbitrarily large. In this paper, we establish an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::316946f81dd286c390f6fb9a46a288b1
https://doi.org/10.1016/j.jde.2019.07.007
https://doi.org/10.1016/j.jde.2019.07.007
Autor:
Longjuan Xu, Hongjie Dong
Publikováno v:
Calculus of Variations and Partial Differential Equations. 60
We consider divergence form, second-order strongly parabolic systems in a cylindrical domain with a finite number of subdomains under the assumption that the interfacial boundaries are $$C^{1,\text {Dini}}$$ and $$C^{\gamma _{0}}$$ in the spatial var
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d1449f73c68ca23a8df26522f2774390
https://doi.org/10.1007/s00526-021-01927-5
https://doi.org/10.1007/s00526-021-01927-5
Autor:
Longjuan Xu, Seick Kim
We construct Green's functions for second order parabolic operators of the form $Pu=\partial_t u-{\rm div}({\bf A} \nabla u+ \boldsymbol{b}u)+ \boldsymbol{c} \cdot \nabla u+du$ in $(-\infty, \infty) \times \Omega$, where $\Omega$ is an open connected
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::be8a30d9d23cbdcf6fb59af7035e96a7
http://arxiv.org/abs/2009.04133
http://arxiv.org/abs/2009.04133
Autor:
Longjuan Xu, Hongjie Dong
In this paper, we show that $W^{1,p}$ $(1\leq p
Comment: 34 pages, submitted
Comment: 34 pages, submitted
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9411dd960910362d90424d196c7653e5
http://arxiv.org/abs/1903.09914
http://arxiv.org/abs/1903.09914
In this paper, we establish the pointwise upper and lower bounds of the gradients of solutions to a class of elliptic systems, including linear systems of elasticity, in a general narrow region and in all dimensions. This problem arises from the stud
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cd0c6fdc28787404a710f8bae6302f33
http://arxiv.org/abs/1808.03384
http://arxiv.org/abs/1808.03384