Zobrazeno 1 - 10
of 27
pro vyhledávání: '"35J94"'
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
We study the behaviour, as $p \to +\infty$, of the second eigenvalues of the $p$-Laplacian with Robin boundary conditions and the limit of the associated eigenfunctions. We prove that, up to some regularity of the set, the limit of the second eigenva
Externí odkaz:
http://arxiv.org/abs/2410.13356
Autor:
Manfredi, Juan J., Mukherjee, Shirsho
We prove the comparison principle for viscosity sub/super-solutions of degenerate subelliptic equations in non-divergence form that include the sub-elliptic infinity Laplacian and the normalized p-Laplacian. The equations are defined by a collection
Externí odkaz:
http://arxiv.org/abs/2409.15144
Autor:
Ercole, Grey
Let $\Omega$ be a bounded, smooth domain of $\mathbb{R}^{N},$ $N\geq2.$ For $p>N$ and $1\leq q(p)<\infty$ set \[ \lambda_{p,q(p)}:=\inf\left\{ \int_{\Omega}\left\vert \nabla u\right\vert ^{p}\mathrm{d}x:u\in W_{0}^{1,p}(\Omega)\text{ \ and \ }\int_{\
Externí odkaz:
http://arxiv.org/abs/2404.17103
Autor:
Backus, Aidan
Motivated by Thurston and Daskalopoulos--Uhlenbeck's approach to Teichm\"uller theory, we study the behavior of $q$-harmonic functions and their $p$-harmonic conjugates in the limit as $q \to 1$, where $1/p + 1/q = 1$. The $1$-Laplacian is already kn
Externí odkaz:
http://arxiv.org/abs/2404.02215
Autor:
Katzourakis, Nikos, Moser, Roger
We study variational problems for second order supremal functionals $\mathrm F_\infty(u)= \|F(\cdot,u,\mathrm D u,\mathrm{A}\!:\!\mathrm D^2u)\|_{\mathrm L^{\infty}(\Omega)}$, where $F$ satisfies certain natural assumptions, $\mathrm A$ is a positive
Externí odkaz:
http://arxiv.org/abs/2403.12625
Autor:
Clark, Ed, Katzourakis, Nikos
We consider the problem of minimising the $L^\infty$ norm of a function of the hessian over a class of maps, subject to a mass constraint involving the $L^\infty$ norm of a function of the gradient and the map itself. We assume zeroth and first order
Externí odkaz:
http://arxiv.org/abs/2303.05944
Autor:
Bungert, Leon
Publikováno v:
Communications in Partial Differential Equations, 48:10-12, 1323-1339, 2024
The purpose of this paper is to prove a uniform convergence rate of the solutions of the $p$-Laplace equation $\Delta_p u = 0$ with Dirichlet boundary conditions to the solution of the infinity-Laplace equation $\Delta_\infty u = 0$ as $p\to\infty$.
Externí odkaz:
http://arxiv.org/abs/2302.08462
In this paper we study the asymptotic behavior of solutions to the subelliptic $p$-Poisson equation as $p\to +\infty$ in Carnot Carath\'eodory spaces. In particular, introducing a suitable notion of differentiability, we extend the celebrated result
Externí odkaz:
http://arxiv.org/abs/2302.03532
We extend some theorems for the Infinity-Ground State and for the Infinity-Potential, known for convex polygons, to other domains in the plane, by applying Alexandroff's method to the curved boundary. A recent explicit solution disproves a conjecture
Externí odkaz:
http://arxiv.org/abs/2301.09022