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Lectures on Elliptic Partial Differential Equations

The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the;

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Elliptic Regularity Theory: A First Course

These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After;

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Regularity Results for Nonlinear Elliptic Systems and Applications

This book collects many helpful techniques for obtaining regularity results for solutions of nonlinear systems of partial differential;

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Stable Solutions of Elliptic Partial Differential Equations

through the fine versions of the maximum principle, the standard regularity theory for linear elliptic equations, and the fundamental functional;

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Stable Solutions of Elliptic Partial Differential Equations

through the fine versions of the maximum principle, the standard regularity theory for linear elliptic equations, and the fundamental functional;

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Elliptic and Parabolic Robin Problems on Lipschitz Domains

The author studies regularity of quasi-linear elliptic and parabolic equations with Robin boundary conditions on Lipschitz domains. He;

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Elliptic Differential Equations

chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue;

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Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48)

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions;

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Strongly Coupled Parabolic and Elliptic Systems

Strongly coupled (or cross-diffusion) systems of parabolic and elliptic partial differential equations appear in many physical applications;

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Direct Methods In The Calculus Of Variations

This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations;

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A Course in Hodge Theory

Offers an examination of the precursors of Hodge theory: first, the studies of elliptic and abelian integrals by Cauchy, Abel, Jacobi, and;

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Partial Differential Equations and Complex Analysis

Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the;

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Partial Differential Equations and Complex Analysis

Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the;

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Analysis, Geometry And Topology Of Elliptic Operators

. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel;

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Elliptic Boundary Value Problems and Construction of Lp-Strong Feller Processes with Singular Drift and Reflection

processes in particular. Topics covered are: Construction of Lp-strong Feller processes using Dirichlet form methods, regularity for solutions;

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Functional Spaces for the Theory of Elliptic Partial Differential Equations

Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions. This book offers on the one hand a complete;

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Elliptic Boundary Value Problems with Fractional Regularity Data

coefficients and for systems of equations. This self-contained exposition of the first order approach offers new results with detailed proofs in a;

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Elliptic Curves. (MN-40), Volume 40

of modular forms and the first connections with elliptic curves. The last two chapters concern Eichler-Shimura theory, which establishes a much;

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Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations

The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions;

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Beyond Sobolev and Besov

, provides a quick guide to function spaces and the general concepts needed. Part II is the heart of the monograph and deals with the regularity;

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Advanced Topics in the Arithmetic of Elliptic Curves

In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that the theory;

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A Hyper graph Regularity Method for Linear Hypergraphs

Szemeredi's Regularity Lemma is a powerful tool in Graph Theory, yielding many applications in areas such as Extremal Graph Theory;

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Ranks of Elliptic Curves and Random Matrix Theory

interplay of number theory and random matrices. It begins with an introduction to elliptic curves and the fundamentals of modelling by a family;

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A Course on Rough Paths: With an Introduction to Regularity Structures

permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox;

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Elliptic Functions

In its first six chapters, this text presents the basic ideas and properties of the Jacobi elliptic functions as a historical essay;

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Lecture Notes On Regularity Theory For The Navier-stokes Equations

of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory;

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Lectures on Pseudo-Differential Operators

function theory in one complex variable and regularity properties of solutions of elliptic partial differential equations. Given here is an;

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