Results 71 to 80 of about 185 (140)

Local Elliptic Regularity for the Dirichlet Fractional Laplacian

Advanced Nonlinear Studies, 2017
We prove the Wloc2⁢s,p${W_{{\mathrm{loc}}}^{2s,p}}$ local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian on an arbitrary bounded open set of ℝN${\mathbb{R}^{N}}$. The key tool consists in analyzing
Biccari Umberto, Warma Mahamadi, Zuazua Enrique   +2 more
doaj   +1 more source

Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness [PDF]

, 2014
In this paper linear stochastic transport and continuity equations with drift in critical Lp spaces are considered. In this situation noise prevents shocks for the transport equation and singularities in the density for the continuity equation, starting ...
Beck, Lisa, Flandoli, Franco, Maurelli, Mario, Gubinelli, Massimilano, Gubinelli, Massimiliano   +4 more
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An unstable elliptic free boundary problem arising in solid combustion

, 2008
We prove a regularity result for the unstable elliptic free boundary problem ∆u = −χ {u>0} (0.1) related to traveling waves in a problem arising in solid combustion. The maximal solution and every local minimizer of the energy are regular, that is, {u
R. Monneau, G. S. Weiss
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Continuity of the temperature in a multi-phase transition problem. [PDF]

Math Ann, 2022
Gianazza U, Liao N.
europepmc   +1 more source

Regular and irregular solutions for a class of elliptic systems in the critical dimension

, 2020
We study regularity properties of weak solutions in the Sobolev space W 1,n 0 to inhomogeneous elliptic systems under a natural growth condition and on bounded Lipschitz domains in R n , i. e.
Lisa Beck, Jens Frehse
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Harnack's inequality for doubly nonlinear equations of slow diffusion type. [PDF]

Calc Var Partial Differ Equ, 2021
Bögelein V, Heran A, Schätzler L, Singer T.   +3 more
europepmc   +1 more source

Singular Solutions of the Capillary Problem

, 1998
The problem of determining the surface interface of fluid partly filling a semi-infinite capillary tube closed at one end is considered, in the absence of gravity.
Robert Weston Neel, Robert Finn
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Global strong solution of compressible flow with spherically symmetric data and density-dependent viscosities

Advances in Nonlinear Analysis
In this article, the Cauchy problem of a compressible Navier-Stokes system with density-dependent viscosities when the initial data are spherically symmetric is considered. Firstly, we construct the classical solution for the system in Ba(t)={r:0≤r≤a(t)}{
Guo Zhenhua, Xu Lei, Zhang Xueyao
doaj   +1 more source

A fractional version of Rivière's GL(n)-gauge. [PDF]

Ann Mat Pura Appl, 2022
Da Lio F, Mazowiecka K, Schikorra A.
europepmc   +1 more source

Ginzburg-Landau Dynamics With A Time-Dependent Magnetic Field

, 1996
. The time-dependent Ginzburg-Landau equations of superconductivity define a dynamical process when the applied magnetic field varies with time. Sufficient conditions (in terms of the time rate of change of the applied field) are given that, if satisfied,
Peter Tak'ac, Hans Kaper
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