A new abstract class of nonlinear resistance forms is defined, with resistance metrics that satisfy the triangle inequality and add over serial circuits, unifying Kigami and p-resistance forms.
The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms
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abstract
In this paper we establish the existence of the extended Dirichlet space for nonlinear Dirichlet forms under mild conditions. We employ it to introduce and characterize criticality (recurrence) and subcriticality (transience) and establish basics of a potential theory.
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Nonlinear resistance forms
A new abstract class of nonlinear resistance forms is defined, with resistance metrics that satisfy the triangle inequality and add over serial circuits, unifying Kigami and p-resistance forms.