Marius Mitrea

Perspectives in Partial Differential Equations, Harmonic Analysis and Applications

A Volume in Honor of Vladimir G. Maz'ya's 70th Birthday

This volume contains a collection of papers contributed on the occasion of Mazya's 70th birthday by a distinguished group of experts of international ...

The Hodge-Laplacian

Boundary Value Problems on Riemannian Manifolds

The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential o...

Layer Potentials, the Hodge Laplacian, and Global Boundary Problems in Nonsmooth Riemannian Manifolds

The general aim of the present monograph is to study boundary-value problems for second-order elliptic operators in Lipschitz sub domains of Riemannia...

Geometric Harmonic Analysis II

Function Spaces Measuring Size and Smoothness on Rough Sets

This monograph is part of a larger program, materializing in five volumes, whose principal aim is to develop tools in Real and Harmonic Analysis, of g...

Groupoid Metrization Theory

With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis

The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on...

Multi-Layer Potentials and Boundary Problems

for Higher-Order Elliptic Systems in Lipschitz Domains

Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator...

Weighted Morrey Spaces

Calderón-Zygmund Theory and Boundary Problems

This monograph is a testament to the potency of the method of singular integrals of layer potential type in solving boundary value problems for weakly...

$L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets

The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local theorem and applying it to sho...

Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces

A Sharp Theory

Systematically constructing an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Alhlfors-regu...

Geometric Harmonic Analysis V

Fredholm Theory and Finer Estimates for Integral Operators, with Applications to Boundary Problems

This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate a...

Layer Potentials, the Hodge Laplacian and Global Boundary Problems in Nonsmooth Riemannian Manifolds

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Geometric Harmonic Analysis I

A Sharp Divergence Theorem with Nontangential Pointwise Traces

This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate a...

Boundary Value Problems for the Stokes System in Arbitrary Lipschitz Domains

The goal of this work is to treat the following main boundary value problems for the Stokes system: (1) the Dirichlet problem with $L^p$-data and nont...

Geometric Harmonic Analysis IV

Boundary Layer Potentials in Uniformly Rectifiable Domains, and Applications to Complex Analysis

This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate a...

Lp-square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets

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