Zobrazeno 1 - 10
of 12 236
pro vyhledávání: '"35J60"'
We propose some general growth conditions on the function $% f=f\left( x,\xi \right) $, including the so-called natural growth, or polynomial, or $p,q-$growth conditions, or even exponential growth, in order to obtain that any local minimizer of the
Externí odkaz:
http://arxiv.org/abs/2410.22875
In this work, we establish sharp and improved regularity estimates for viscosity solutions of Hardy-H\'{e}non-type equations with possibly singular weights and strong absorption governed by the $\infty$-Laplacian $$ \Delta_{\infty} u(x) = |x|^{\alpha
Externí odkaz:
http://arxiv.org/abs/2410.19970
This paper is concerned with a comparison principle for viscosity solutions to Hamilton-Jacobi (HJ), -Bellman (HJB), and -Isaacs (HJI) equations for general classes of partial integro-differential operators. Our approach innovates in three ways: (1)
Externí odkaz:
http://arxiv.org/abs/2410.19566
Autor:
Choi, Wonhyung, Ahn, Inkyung
Understanding species dynamics in heterogeneous environments is essential for ecosystem studies. Traditional models assumed homogeneous habitats, but recent approaches include spatial and temporal variability, highlighting species migration. We adopt
Externí odkaz:
http://arxiv.org/abs/2410.18621
We present a method of solving a nonlinear Dirichlet problem with discontinuous boundary data and we give a probabilistic representation of the solution using the nonlocal branching process associated with the nonlinear term of the operator. Instead
Externí odkaz:
http://arxiv.org/abs/2410.16988
The $\sigma_k(A_g)$ curvature and the boundary $\mathcal{B}^k_g$ curvature arise naturally from the Chern--Gauss--Bonnet formula for manifolds with boundary. In this paper, we prove a Liouville theorem for the equation $\sigma_k(A_g)=1$ in $\overline
Externí odkaz:
http://arxiv.org/abs/2410.16384
Autor:
McCleerey, Nicholas
Given a psh function $\varphi\in\mathcal{E}(\Omega)$ and a smooth, bounded $\theta\geq 0$, it is known that one can solve the Monge-Amp\`{e}re equation $\mathrm{MA}(\varphi_\theta)=\theta^n\mathrm{MA}(\varphi)$, with some form of Dirichlet boundary v
Externí odkaz:
http://arxiv.org/abs/2410.15202
Autor:
Chernysh, Edward
We establish Struwe-type decompositions of Palais-Smale sequences for a class of critical $p$-Laplace equations of the Caffarelli-Kohn-Nirenberg type in a bounded domain $\Omega\subset\mathbb{R}^n$, $n\ge2$, containing the origin. In doing so, we hig
Externí odkaz:
http://arxiv.org/abs/2410.14861
Autor:
Xu, Jie
Let $ (M, g) $ be a compact manifold or a complete non-compact manifold without boundary, $ \dim M \geqslant 4 $, and not locally conformally flat. In this article, we introduce a new local method to resolve the Yamabe problem on compact manifold for
Externí odkaz:
http://arxiv.org/abs/2410.13537
Autor:
Calamai, Alessandro, Infante, Gennaro
We investigate the existence of nontrivial solutions of parameter-dependent elliptic equations with deviated argument in annular-like domains in $\mathbb{R}^{n}$, with $n\geq 2$, subject to functional boundary conditions. In particular we consider a
Externí odkaz:
http://arxiv.org/abs/2410.11615