Nonlinear resistance forms

2025/07/04 by Puchert, Simon, Schmidt, Marcel
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2507.03426

Abstract

In this paper we introduce the notion of nonlinear resistance forms. We define a 1-parameter family of nonlinear resistance metrics and show their additivity over serial circuits. Moreover, we prove that resistance forms and p-resistance forms fall into our framework.

Citations

• Nonlinear Beurling-Deny criteria
• The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms
• Contraction properties and differentiability of p-energy forms with applications to nonlinear potential theory on self-similar sets
• Weak monotonicity property of Korevaar-Schoen norms on nested fractals
• First-order Sobolev spaces, self-similar energies and energy measures on the Sierpiński carpet
• Korevaar-Schoen-Sobolev spaces and critical exponents in metric measure spaces
• Sobolev spaces and Poincaré inequalities on the Vicsek fractal
• p-energies on p.c.f. self-similar sets
• Conductive homogeneity of compact metric spaces and construction of p-energy
• Nonlinear Evolution Equation Associated with Hypergraph Laplacian
• Cheng maximal diameter theorem for hypergraphs
• Finding Cheeger Cuts in Hypergraphs via Heat Equation
• Diffusion Operator and Spectral Analysis for Directed Hypergraph Laplacian
• Energy forms

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• Effective Resistance in Simplicial Complexes as Bilinear Forms: Generalizations and Properties