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Now showing items 1-10 of 13

#### $L^p$-bounds for pseudo-differential operators on compact Lie groups

Given a compact Lie group $G$, in this paper we establish $L^p$-bounds for pseudo-differential operators in $L^p(G)$. The criteria here are given in terms of the concept of matrix symbols defined on the non-commutative ...

#### Hardy and Rellich inequalities for anisotropic p-sub-Laplacians

In this paper we establish the subelliptic Picone type identities. As consequences, we obtain Hardy and Rellich type inequalities for anisotropic p-sub- Laplacians which are operators of the form $$ \mathcal{L}_p f := ...

#### Difference equations and pseudo-differential operators on $\mathbb{Z}^n$

In this paper we develop the calculus of pseudo-differential operators on the lattice $\mathbb{Z}^n$, which we can call pseudo-difference operators. An interesting feature of this calculus is that the phase space is compact ...

#### Bubbling analysis and geometric convergence results for free boundary minimal surfaces

(Ecole polytechnique, 2019-08-28)

We investigate the limit behaviour of sequences of free boundary minimal hypersurfaces with bounded index and volume, by presenting a detailed blow-up analysis near the points where curvature concentration occurs. Thereby, ...

#### The heat equation with singular potentials

We consider the heat equation with strongly singular potentials and prove that it has a "very weak solution". Moreover, we show the uniqueness and consistency results in some appropriate senses. The cases of positive and ...

#### Time-dependent wave equations on graded groups

(Springer, 2021-02)

In this paper we consider the wave equations for hypoelliptic homogeneous left-invariant operators on graded Lie groups with time-dependent H\"older propagation speeds. The examples are the time-dependent wave equation for ...

#### Eigenfunction expansions of ultradifferentiable functions and ultradistributions. III. Hilbert spaces and Universality

(Springer, 2021-03)

In this paper we analyse the structure of the spaces of smooth type functions, generated by elements of arbitrary Hilbert spaces, as a continuation of the research in our previous papers in this series. We prove that these ...

#### Reverse integral Hardy inequality on metric measure spaces

(Academia Scientiarum Fennica, 2021)

In this note, we obtain a reverse version of the integral Hardy inequality on metric measure spaces. Moreover, we give necessary and sufficient conditions for the weighted reverse Hardy inequality to be true. The main tool ...

#### Dressing with Control: using integrability to generate desired solutions to Einstein's equations

(2014-06-16)

Motivated by integrability of the sine-Gordon equation, we investigate a technique for constructing desired solutions to Einstein's equations by combining a dressing technique with a control-theory approach. After reviewing ...

#### Direct and Inverse problems for time-fractional pseudo-parabolic equations

The purpose of this paper is to establish the solvability results to direct and inverse problems for time-fractional pseudo-parabolic equations with the self-adjoint operators. We are especially interested in proving ...