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Compressible Navier–Stokes–Fourier flows at steady-state
The heat conducting compressible viscous flows are governed by the Navier–Stokes–Fourier (NSF) system. In this paper, we study the NSF system...
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Multilinear Calderón-Zygmund operators and their commutators with BMO functions in variable exponent Morrey spaces
The boundedness of multilinear Calderón-Zygmund operators and their commutators with bounded mean oscillation (BMO) functions in variable exponent...
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Applications to Analysis in Several Complex Variables
In this chapter we shall present a multitude of applications of the body of results developed so far in the area of Geometric Harmonic Analysis to...
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Hilbert’s \(19{\text {th}}\) problem revisited
In this survey article we revisit Hilbert’s 19th problem concerning the regularity of minimizers of variational integrals. We first discuss the...
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Various Function Spaces
In recent decades, the subject of function spaces has undergone a rapid diversification and expansion, though the decomposition of functions and...
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Regularity of Weak Solutions to Nondiagonal Elliptic Systems with Composite Boundary Conditions
We consider a model problem in a half-ball for linear and quasilinear elliptic systems of equations with nondiagonal principal matrix. It is assumed...
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Appendices
We recall standard properties of Sobolev spaces used throughout the book, and we gather the most technical parts of some of the proofs presented in...
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Nonuniformly elliptic Schauder theory
Local Schauder theory holds in the nonuniformly elliptic setting. Specifically, first derivatives of solutions to nonuniformly elliptic problems are...
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Global Solvability of the Cauchy-Dirichlet Problem for a Class of Strongly Nonlinear Parabolic Systems
We consider a class of nonlinear parabolic systems for elliptic operators of variational structure with nondiagonal principal matrices. Additional...
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Calderón’s First and Second Complex Interpolations of Closed Subspaces of Morrey Spaces
In this paper, we are going to describe the first and second complex interpolations of closed subspaces of Morrey spaces, based on our previous...
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Fundamentals
This introductory chapter contains a brief review of the theory of real and complex manifolds, including the basics of holomorphic approximation...
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Compactness for the commutators of multilinear singular integral operators with non-smooth kernels
In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of...
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Weighted Lorentz estimates for parabolic equations with non-standard growth on rough domains
The main aim of this paper is to prove the Calderón–Zygmund estimates for a general nonlinear parabolic equation of p ( x , t )-Laplacian type in the...
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Two-Phase Problem for Quasilinear Parabolic Systems with Nondiagonal Principal Matrix. Regularity of Weak Solutions
We study the regularity of weak solutions to the two-phase the problem for quasilinear parabolic systems with nondiagonal principal matrices. We...
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A criterion for embedding of anisotropic Sobolev–Morrey spaces into the space of uniformly continuous functions
We prove the embedding theorems of the Sobolev–Morrey spaces into the space of uniformly continuous functions so extending the classical Sobolev...