Related papers: $p$-Energy forms on fractals: recent progress

We study vortices in p-wave superconductors in a Ginzburg-Landau setting. The state of the superconductor is described by a pair of complex wave functions, and the p-wave symmetric energy functional couples these in both the kinetic…

We provide a definition of integral, along paths in the Sierpinski gasket K, for differential smooth 1-forms associated to the standard Dirichlet form K. We show how this tool can be used to study the potential theory on K. In particular,…

We initiate the study of fine $p$-(super)minimizers, associated with $p$-harmonic functions, on finely open sets in metric spaces, where $1 < p < \infty$. After having developed their basic theory, we obtain the $p$-fine continuity of the…

The modeling of fracture problems within geometrically linear elasticity is often based on the space of generalized functions of bounded deformation $GSBD^p(\Omega)$, $p\in(1,\infty)$, their treatment is however hindered by the very low…

This paper deals with the variational analysis, for every $s \in (0,1)$ and $p \in [1,+\infty)$, of $(s,p)$-Gagliardo seminorms in a periodic setting. First, we consider the space of $L^p$, $T$-periodic functions and define the energy…

The theory of p-adic fractal strings and their complex dimensions was developed by the first two authors in [17, 18, 19], particularly in the self-similar case, in parallel with its archimedean (or real) counterpart developed by the first…

We study energy measures of canonical Dirichlet forms on inhomogeneous Sierpinski gaskets. We prove that the energy measures and suitable reference measures are mutually singular under mild assumptions.

Let $(X,d,\mu)$ be a doubling metric measure space endowed with a Dirichlet form $\E$ deriving from a "carr\'e du champ". Assume that $(X,d,\mu,\E)$ supports a scale-invariant $L^2$-Poincar\'e inequality. In this article, we study the…

We discuss quantitative estimates of the local spectral dimension of the two-dimensional Sierpinski gasket. The present arguments were inspired by a previous study of the distribution of the Kusuoka measure by R. Bell, C.-W. Ho, and R. S.…

In this paper, we establish the existence of $p$-energy norms and the corresponding $p$-energy measures for scale-irregular Vicsek sets, which may lack self-similarity. We also investigate the characterizations of $p$-energy norms in terms…

The theory of Dirichlet forms as originated by Beurling-Deny and developed particularly by Fukushima and Silverstein, is a natural functional analytic extension of classical (and axiomatic) potential theory. Although some parts of it have…

In this paper we extend and complement some recent results by Chiodaroli, De Lellis and Kreml on the well-posedness issue for weak solutions of the compressible isentropic Euler system in $2$ space dimensions with pressure law…

This work provides an extension of parts of the classical finite dimensional sub-elliptic theory in the context of infinite dimensional compact connected metrizable groups. Given a well understood and well behaved bi-invariant Laplacian,…

We affirmatively resolve the energy image density conjecture of Bouleau and Hirsch (1986). Beyond the original framework of Dirichlet structures, we establish the energy image density property in several related settings. In particular, we…

The non extensive aspects of $p_T$ distributions obtained in high energy collisions are discussed in relation to possible fractal structure in hadrons, in the sense of the thermofractal structure recently introduced. The evidences of…

For $p>1$, and for a $p$-energy on a metric measure space, we provide various geometric and functional conditions for the validity of the cutoff Sobolev inequality. In particular, we employ a technique of Trudinger and Wang [Amer. J. Math.…

This is the first of a pair of papers, whose collective goal is to disprove a conjecture of Kemarsky, Paulin, and Shapira (KPS) on the escape of mass of Laurent series. This paper lays the foundations on which its sibling builds. In…

In 1981, Sacks and Uhlenbeck introduced their famous $\alpha$-energy as a way to approximate the Dirichlet energy and produce harmonic maps from surfaces into Riemannian manifolds. However, the second and third authors together with…

We study a formulation of Burgers equation on the Sierpinski gasket, which is the prototype of a p.c.f. self-similar fractal. One possibility is to implement Burgers equation as a semilinear heat equation associated with the Laplacian for…

In this paper we consider sequences of $p$-harmonic maps, $p>2$, from a closed Riemann surface $\Sigma$ into the $n$-dimensional sphere $\mathbb{S}^n$ with uniform bounded energy. These are critical points of the energy $E_p(u)…