Zobrazeno 1 - 10
of 256
pro vyhledávání: '"Bao, Jiguang"'
Autor:
Wang, Cong, Bao, Jiguang
The present paper provides two necessary and sufficient conditions for the existence of solutions to the exterior Dirichlet problem of the Monge-Amp\`ere equation with prescribed asymptotic behavior at infinity. By an adapted smooth approximation arg
Externí odkaz:
http://arxiv.org/abs/2401.11690
Autor:
Li, Xiang, Bao, Jiguang
In this paper, we give some existence and nonexistence results for nonradial entire large solutions of the Hessian equation $S_k\left(D^2 u\right)=b(x) u^\gamma$ in the sublinear case $0<\gamma
Externí odkaz:
http://arxiv.org/abs/2310.09579
In this paper, we obtain the interior derivative estimates of solutions for elliptic and parabolic Hessian quotient equations. Then we establish the Bernstein theorem for parabolic Hessian quotient equations, that is, any parabolically convex solutio
Externí odkaz:
http://arxiv.org/abs/2305.17831
The Liouville type theorem on the parabolic Monge--Amp\`ere equation $-u_t\det D^2u=1$ states that any entire parabolically convex classical solution must be of form $-t+|x|^2/2$ up to a re-scaling and transformation, under additional assumption that
Externí odkaz:
http://arxiv.org/abs/2305.08329
In this paper, we establish the existence and uniqueness theorem of entire solutions to the Lagrangian mean curvature equations with prescribed asymptotic behavior at infinity. The phase functions are assumed to be supercritical and converge to a con
Externí odkaz:
http://arxiv.org/abs/2302.06987
In this paper, we establish the gradient and Pogorelov estimates for $k$-convex-monotone solutions to parabolic $k$-Hessian equations of the form $-u_t\sigma_k(\lambda(D^2u))=\psi(x,t,u)$. We also apply such estimates to obtain a Liouville type resul
Externí odkaz:
http://arxiv.org/abs/2209.10776
In this paper, we study the exterior Dirichlet problem for the fully nonlinear elliptic equation $f(\lambda(D^{2}u))=1$. We obtain the necessary and sufficient conditions of existence of radial solutions with prescribed asymptotic behavior at infinit
Externí odkaz:
http://arxiv.org/abs/2206.09095
In this paper, we study the Dirichlet problem of Hessian quotient equations in exterior domains. By estimating the eigenvalues of the solution, the necessary and sufficient conditions on existence of radial solutions are obtained. Applying the soluti
Externí odkaz:
http://arxiv.org/abs/2206.09069
In this paper, we discuss the more general Hessian inequality $\sigma_{k}^{\frac{1}{k}}(\lambda (D_i (A\left(|Du|\right) D_j u)))\geq f(u)$ including the Laplacian, p-Laplacian, mean curvature, Hessian, k-mean curvature operators, and provide a neces
Externí odkaz:
http://arxiv.org/abs/2205.08415
Autor:
Wang, Cong, Bao, Jiguang
In this paper, we establish the existence and uniqueness theorem for entire solutions of Hessian equations with prescribed asymptotic behavior at infinity. This extends the previous results on Monge-Amp\`{e}re equations. Our approach also makes the p
Externí odkaz:
http://arxiv.org/abs/2203.02646