Search results for "potential theory"
showing 10 items of 24 documents
Harmonic morphisms in nonlinear potential theory
1992
This article concerns the following problem: given a family of partial differential operators with similar structure and given a continuous mapping f from an open set Ω in Rn into Rn, then when does f pull back the solutions of one equation in the family to solutions of another equation in that family? This problem is typical in the theory of differential equations when one wants to use a coordinate change to study solutions in a different environment.
Spontaneous periodic and bursting current oscillations in iron corrosion by dichromate: a useful study for simulating biological systems
1995
Abstract Studies on chemical and electrochemical oscillating systems are very useful in understanding more complex biological systems. Spontaneous periodic and bursting current oscillations were found in iron/dichromate systems coupled with graphite or zinc electrodes. In this paper, we study some phenomenological features of the two systems: their typical oscillation profiles and the influence of external resistance. The results are explained by the Franck-Fitzhugh model using the mixed potential theory.
Nonlinear Potential Theory and PDEs
1994
We consider equations like — div(∣∇u∣ p-2∇u) = µ, where µ is a nonnegative Radon measure and 1 < p < ∞. Results that relate the solution u and the measure µ are reviewed. A link between potential estimates and the boundary regularity of the Dirichlet problem is established.
A non-linear version of Hunt-Lion's theorem from the point of view of T-accretivity
1992
In the classical topological context, Dellacherie [10] has given a non-linear version of Hunt's theorem characterizing the proper kernels verifying the complete maximum principle as those closing a submarkovian resolvent. In this paper we study the relation between this non-linear version of Hunt's theorem and T-accretivity.
H�lder continuity of solutions to quasilinear elliptic equations involving measures
1994
We show that the solutionu of the equation $$ - div(|\nabla u|^{p - 2} \nabla u) = \mu $$ is locally β-Holder continuous provided that the measure μ satisfies the condition μ(B(x,r))⩽Mrn − p + α(p − 1) for some α>β. A corresponding result for more general operators is also proven.
Curve packing and modulus estimates
2018
A family of planar curves is called a Moser family if it contains an isometric copy of every rectifiable curve in $\mathbb{R}^{2}$ of length one. The classical "worm problem" of L. Moser from 1966 asks for the least area covered by the curves in any Moser family. In 1979, J. M. Marstrand proved that the answer is not zero: the union of curves in a Moser family has always area at least $c$ for some small absolute constant $c > 0$. We strengthen Marstrand's result by showing that for $p > 3$, the $p$-modulus of a Moser family of curves is at least $c_{p} > 0$.
The Obstacle Problem in a Non-Linear Potential Theory
1988
M. Brelot gave rise to the concept harmonic space when he extended classical potential theory on ℝn to an axiomatic system on a locally compact space. I have recently constructed1 a non-linear harmonic space by dropping the assumption that the sum of two harmonic functions is harmonic and considering some other axioms instead. This approach has its origin in the work of O. Martio, P. Lindqvist and S. Granlund2,3,4, who have developed a non-linear potential theory on ℝn connected with variational integrals of the type ∫ F(x,∇u(x)) dm(x), where F(x, h) ≈ |h|p.
Failure of topological rigidity results for the measure contraction property
2014
We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. The first one satisfies MCP(0,3) and contains a subset isometric to $\mathbb{R}$, but does not topologically split. The second space satisfies MCP(2,3) and has diameter $\pi$, which is the maximal possible diameter for a space satisfying MCP(N-1,N), but is not a topological spherical suspension. The latter example gives an answer to a question by Ohta.
CVBEM application to a novel potential function providing stress field and twist rotation at once
2013
AbstractIn this paper, complex variable boundary element method (CVBEM) is used for the solution of de Saint-Venant’s torsion problem in homogenous isotropic elastic beams with a generic cross section, considering a complex potential function related to the stress field. Generally, CVBEM, when used for torsion problems, leads to evaluation of the stress field divided by the twist rotation. The latter has been evaluated by performing a domain integral. In this paper, taking advantage of the aforementioned potential function, it is possible, by applying CVBEM, to evaluate the complete stress distribution and the twist rotation of the cross section and the torsional stiffness factor, performin…
A note on an overdetermined problem for the capacitary potential
2016
We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.