The p-Laplacian evolution equation in metric measure spaces has been studied as the gradient flow L2 of p-Cheeger energy (for 1<p<∞). In this paper, using first-order differential structure on a space introduced by Gigli, we characterise subdifferential energy. This gives rise to new definition operator spaces, which allows us work with more detail. way, introduce notion solutions spaces. For p...

We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.

The domination properties of the Laplace operator on a class of symmetric spaces of noncom-pact type are investigated. Using algebraic methods we will show that derivatives of a function can be uniformly estimated by function and its Laplacian in L p spaces for all 1 p 1. We will also discuss some relative aspects of the theory of convolutions.

A new derivation is given of Branson’s factorization formula for the conformally invariant operator on the sphere whose principal part is the k-th power of the scalar Laplacian. The derivation deduces Branson’s formula from knowledge of the corresponding conformally invariant operator on Euclidean space (the k-th power of the Euclidean Laplacian) via conjugation by the stereographic projection ...

In this paper we study the local Lipschitz regularity of weak solutions to certain singular elliptic equations involving one-Laplacian. Equations treated here also contains another well-behaving operator such as $$p$$ -Laplacian with $$1<p<\infty $$ . The problem is that one-Laplacian too on degenerate points, what often called a facet, which makes it difficult obtain even solutions. This diffi...