Results 131 to 140 of about 43,034 (224)

Explicit solutions of Jensen's auxiliary equations via extremal Lipschitz extensions

Electronic Journal of Differential Equations, 2020
In this note we prove that McShane and Whitney's Lipschitz extensions are viscosity solutions of Jensen's auxiliary equations which are known to have a key role in Jensen's celebrated proof of uniqueness of infinity harmonic functions, and therefore ...
Fernando Charro
doaj  

Harmonic maps to the circle with higher dimensional singular set

Proceedings of the London Mathematical Society, Volume 132, Issue 3, March 2026.
Abstract In a closed, oriented ambient manifold (Mn,g)$(M^n,g)$ we consider the problem of finding S1$\mathbb {S}^1$‐valued harmonic maps with prescribed singular set. We show that the boundary of any oriented (n−1)$(n-1)$‐submanifold can be realised as the singular set of an S1$\mathbb {S}^1$‐valued map, which is classically harmonic away from the ...
Marco Badran
wiley   +1 more source

Weakly Increasing Solutions of Equations with p-Mean Curvature Operator

Mathematics
Globally positive unbounded solutions, with zero derivative at infinity, are here considered for ordinary differential equations involving the generalized Euclidean mean curvature operator.
Zuzana Došlá, Mauro Marini, Serena Matucci   +2 more
doaj   +1 more source

Coloring and density theorems for configurations of a given volume

Proceedings of the London Mathematical Society, Volume 132, Issue 3, March 2026.
Abstract This is a treatise on finite point configurations spanning a fixed volume to be found in a single color‐class of an arbitrary finite (measurable) coloring of the Euclidean space Rn$\mathbb {R}^n$, or in a single large measurable subset A⊆Rn$A\subseteq \mathbb {R}^n$.
Vjekoslav Kovač
wiley   +1 more source

Cut Finite Element 3D Acoustic Shape Optimization of a Compression Driver Taking Viscothermal Losses Into Account

International Journal for Numerical Methods in Engineering, Volume 127, Issue 4, 28 February 2026.
ABSTRACT Wave propagation effects such as resonance and interference effects complicate the design of many acoustic devices, particularly when the dimensions of the device are in the order of the operating wavelength. At the same time, these complications also offer an opportunity for numerical optimization schemes to outperform designs achieved using ...
Martin Berggren, Anders Bernland, André Massing, Daniel Noreland, Eddie Wadbro   +4 more
wiley   +1 more source

Boundary differentiability for inhomogeneous infinity Laplace equations

Electronic Journal of Differential Equations, 2014
We study the boundary regularity of the solutions to inhomogeneous infinity Laplace equations. We prove that if $u\in C(\bar{\Omega})$ is a viscosity solution to $\Delta_{\infty}u:=\sum_{i,j=1}^n u_{x_i}u_{x_j}u_{x_ix_j}=f$ with $f\in C(\Omega)\cap L^
Guanghao Hong
doaj  

A Boundary Harnack Principle for Infinity-Laplacian and Some Related Results

Boundary Value Problems, 2007
We prove a boundary comparison principle for positive infinity-harmonic functions for smooth boundaries. As consequences, we obtain (a) a doubling property for certain positive infinity-harmonic functions in smooth bounded domains and the half-space ...
Bhattacharya Tilak
doaj  

C-infinity interfaces of solutions for one-dimensional parabolic p-Laplacian equations

Electronic Journal of Differential Equations, 1999
We study the regularity of a moving interface $x = zeta (t)$ of the solutions for the initial value problem $$ u_t = left(|u_x|^{p-2}u_x ight)_x quad u(x,0) =u_0 (x),, $$ where $u_0in L^1({Bbb R})$ and $p>2$.
Yoonmi Ham, Youngsang Ko
doaj  

Partial differential equations in data science. [PDF]

Philos Trans A Math Phys Eng Sci
Bertozzi AL, Drenska N, Latz J, Thorpe M.   +3 more
europepmc   +1 more source