Zobrazeno 1 - 10
of 583
pro vyhledávání: '"Dong, Hongjie"'
In this paper, we are concerned with divergence form, higher-order parabolic systems in a cylindrical domain with a finite number of subdomains. We establish $L_\infty$ and Schauder estimates of solutions when the leading coefficients and the non-hom
Externí odkaz:
http://arxiv.org/abs/2407.17733
Autor:
Bulut, Aynur, Dong, Hongjie
We study the global well-posedness of the supercritical dissipative surface quasi-geostrophic (SQG) equation, a key model in geophysical fluid dynamics. While local well-posedness is known, achieving global well-posedness for large initial data remai
Externí odkaz:
http://arxiv.org/abs/2402.19439
This paper investigates the Dirichlet problem for a non-divergence form elliptic operator $L$ in a bounded domain of $\mathbb{R}^d$. Under certain conditions on the coefficients of $L$, we first establish the existence of a unique Green's function in
Externí odkaz:
http://arxiv.org/abs/2402.17948
We investigate the regularity of elliptic equations in double divergence form, with leading coefficients satisfying the Dini mean oscillation condition. We prove that the solutions are differentiable on the zero level set and derive a pointwise bound
Externí odkaz:
http://arxiv.org/abs/2401.06621
The control of plasma-wall interaction is one of the keys in a fusion device from both physical and mathematical standpoints. A classical perfect conducting boundary causes the Lorentz force to penetrate inside the domain, which may lead to grazing s
Externí odkaz:
http://arxiv.org/abs/2401.00554
We study the perfect conductivity problem with closely spaced perfect conductors embedded in a homogeneous matrix where the current-electric field relation is the power law $J=\sigma|E|^{p-2}E$. The gradient of solutions may be arbitrarily large as $
Externí odkaz:
http://arxiv.org/abs/2311.11541
In this paper, we study degenerate or singular elliptic equations in divergence form $$-\text{div}(x_n^\alpha A\nabla u)=\text{div}(x_n^\alpha \mathbf{g})\quad\text{in }B_1\cap\{x_n>0\}.$$ When $\alpha>-1$, we establish boundary Schauder type estimat
Externí odkaz:
http://arxiv.org/abs/2311.06846
Autor:
Dong, Hongjie, Kitano, Shuhei
We obtain new $L_p$ estimates for subsolutions to fully nonlinear equations. Based on our $L_p$ estimates, we further study several topics such as the third and fourth order derivative estimates for concave fully nonlinear equations, critical exponen
Externí odkaz:
http://arxiv.org/abs/2311.04399
We prove the local-in-time well-posedness of the relativistic Vlasov-Maxwell-Landau system in a bounded domain $\Omega$ with the specular reflection condition. Our result covers the case when $\Omega$ is a non-convex domain, e.g., solid torus. To the
Externí odkaz:
http://arxiv.org/abs/2310.07192
In this paper, we consider higher regularity of a weak solution $({\bf u},p)$ to stationary Stokes systems with variable coefficients. Under the assumptions that coefficients and data are piecewise $C^{s,\delta}$ in a bounded domain consisting of a f
Externí odkaz:
http://arxiv.org/abs/2309.06722