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Existence of an entropic solution of a nonlinear elliptic problem in an unbounded domain
AbstractWe consider a second-order quasilinear elliptic equation with an integrable right-hand side. We formulate constraints on the structure of...
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Lipschitz Continuous Solutions of the Vlasov–Maxwell Systems with a Conductor Boundary Condition
We consider relativistic plasma particles subjected to an external gravitation force in a 3D half space whose boundary is a perfect conductor. When...
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Lipschitz Continuity of Solutions to Drift-Diffusion Equations in the Presence of Nonlocal Terms
We analyze the propagation of Lipschitz continuity of solutions to various linear and nonlinear drift-diffusion systems, with and without...
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Lipschitz Bounds and Nonautonomous Integrals
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting...
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Asymptotic Stability of Precessing Domain Walls for the Landau–Lifshitz–Gilbert Equation in a Nanowire with Dzyaloshinskii–Moriya Interaction
We consider a ferromagnetic nanowire and we focus on an asymptotic regime where the Dzyaloshinskii-Moriya interaction is taken into account. First we...
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Ergodicity for the Randomly Forced Navier–Stokes System in a Two-Dimensional Unbounded Domain
The ergodic properties of the randomly forced Navier–Stokes system have been extensively studied in the literature during the last two decades. The...
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Wavelet Transform of Dini Lipschitz Functions on the Quaternion Algebra
In this present work, we generalize Titchmarsh’s theorem for the complex- or hypercomplex-valued functions. Firstly, we examine the order of...
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Transverse Domain Walls in Thin Ferromagnetic Strips
We present a characterization of the domain wall solutions arising as minimizers of an energy functional obtained in a suitable asymptotic regime of...
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Multidimensional Zaremba problem for the \(p(\,\cdot\,)\)-Laplace equation. A Boyarsky–Meyers estimate
AbstractWe prove the higher integrability of the gradient of solutions of the Zaremba problem in a bounded strongly Lipschitz domain for an...
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Spectral Gap Formation to Kinetic Equations with Soft Potentials in Bounded Domain
It has been unknown in kinetic theory whether the linearized Boltzmann or Landau equation with soft potentials admits a spectral gap in the spatially...
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Conditional \(L^{\infty }\) Estimates for the Non-cutoff Boltzmann Equation in a Bounded Domain
We consider weak solutions of the inhomogeneous non-cutoff Boltzmann equation in a bounded domain with any of the usual physical boundary conditions:...
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No-Slip Boundary Condition for Vorticity Equation in 2D Exterior Domain
In this article we derive the no-slip boundary condition for a non-stationary vorticity equation. This condition generates the affine invariant...
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Extension of the Günter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves
Regularization techniques for the trace and the traction of elastic waves potentials previously built for domains of the class C 2 are extended to the...
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Construction of a Right Inverse for the Divergence in Non-cylindrical Time Dependent Domains
We construct a stable right inverse for the divergence operator in non-cylindrical domains in space-time. The domains are assumed to be Hölder...
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The Asymptotically Sharp Geometric Rigidity Interpolation Estimate in Thin Bi-Lipschitz Domains
This work is part of a program of development of asymptotically sharp geometric rigidity estimates for thin domains. A thin domain in three...
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Dissipation in Onsager’s Critical Classes and Energy Conservation in \(BV\cap L^\infty \) with and Without Boundary
This paper is concerned with the incompressible Euler equations. In Onsager’s critical classes we provide explicit formulas for the Duchon–Robert...
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Weyl’s Law for the Steklov Problem on Surfaces with Rough Boundary
The validity of Weyl’s law for the Steklov problem on domains with Lipschitz boundary is a well-known open question in spectral geometry. We answer...