Existence and regularity of the solutions to degenerate elliptic equations in Carnot-Carathéodory spaces
Sign Up to like & getrecommendations! Published in 2020 at "Banach Journal of Mathematical Analysis"
DOI: 10.1007/s43037-020-00069-8
Abstract: We deal with existence and regularity for weak solutions to Dirichlet problems of the type $$\begin{aligned} \left\{ \begin{array}{ll} - \mathrm{div} (A(x)Xu) +b(x)Xu + c(x)u=f\quad \hbox {in} \; \varOmega \\ \\ u=0 \quad \quad \hbox {on}… read more here.
Keywords: solutions degenerate; degenerate elliptic; regularity solutions; existence regularity ... See more keywords
On the maximal L-L regularity of solutions to a general linear parabolic system
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2019.09.058
Abstract: We show the existence of solution in the maximal $L_p-L_q$ regularity framework to a class of symmetric parabolic problems on a uniformly $C^2$ domain in ${\mathcal R}$. Our approach consist in showing ${\mathcal R}$ -… read more here.
Keywords: maximal regularity; linear parabolic; regularity; general linear ... See more keywords
Regularity of solutions to the fractional Cheeger-Laplacian on domains in metric spaces of bounded geometry
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2021.10.029
Abstract: We study existence, uniqueness, and regularity properties of the Dirichlet problem related to fractional Dirichlet energy minimizers in a complete doubling metric measure space $(X,d_X,\mu_X)$ satisfying a $2$-Poincare inequality. Given a bounded domain $\Omega\subset X$… read more here.
Keywords: solutions fractional; theta; geometry; regularity solutions ... See more keywords
Sobolev regularity of solutions of the cohomological equation
Sign Up to like & getrecommendations! Published in 2021 at "Ergodic Theory and Dynamical Systems"
DOI: 10.1017/etds.2019.108
Abstract: In this survey we prove the sharpest results on the loss of Sobolev regularity for solutions of the cohomological equation for translation flows on translation surfaces, available to the methods developed by the author in… read more here.
Keywords: cohomological equation; regularity solutions; solutions cohomological; sobolev regularity ... See more keywords
Higher regularity of solutions of singular parabolic equations with variable nonlinearity
Sign Up to like & getrecommendations! Published in 2019 at "Applicable Analysis"
DOI: 10.1080/00036811.2017.1382690
Abstract: ABSTRACT We study the global regularity of solutions of the homogeneous Dirichlet problem for the parabolic equation with variable nonlinearity where p(x, t), are given functions of their arguments, and . Conditions on the data… read more here.
Keywords: higher regularity; variable nonlinearity; regularity solutions; solutions singular ... See more keywords
Regularity of solutions to 1D compressible Navier–Stokes–Allen–Cahn system
Sign Up to like & getrecommendations! Published in 2019 at "Applicable Analysis"
DOI: 10.1080/00036811.2019.1668554
Abstract: In this paper, we investigate the compressible Navier–Stokes equations coupled with an Allen–Cahn phase field description, which describes two-phase patterns in a flowing liquid including phase transformations. Our purpose is to establish the regularity of… read more here.
Keywords: compressible navier; stokes allen; allen cahn; cahn system ... See more keywords
Existence and Regularity of Solutions for Some Partial Integrodifferential Equations Involving the Nonlocal Conditions
Sign Up to like & getrecommendations! Published in 2019 at "Numerical Functional Analysis and Optimization"
DOI: 10.1080/01630563.2019.1604547
Abstract: Abstract The aim of this work is to prove some results about the existence and regularity of solutions for some partial integrodifferential equations with nonlocal conditions. We suppose that the linear part has a resolvent… read more here.
Keywords: integrodifferential equations; nonlocal conditions; existence regularity; partial integrodifferential ... See more keywords
On the regularity of solutions to the Beltrami equation in the Plane
Sign Up to like & getrecommendations! Published in 2019 at "Complex Variables and Elliptic Equations"
DOI: 10.1080/17476933.2018.1427084
Abstract: ABSTRACT We obtain interior estimates on regularity of solutions to the inhomogeneous Beltrami equation in the plane, namely when h and the coefficients and are Dini continuous; the coefficients satisfy an ellipticity condition . read more here.
Keywords: beltrami equation; equation plane; regularity solutions;
Existence, multiplicity and regularity of solutions for the fractional $p$-Laplacian equation
Sign Up to like & getrecommendations! Published in 2020 at "Journal of The Korean Mathematical Society"
DOI: 10.4134/jkms.j190693
Abstract: We are concerned with the following elliptic equations: { (−∆)pu = λf(x, u) in Ω, u = 0 on RN\Ω, where λ are real parameters, (−∆)p is the fractional p-Laplacian operator, 0 < s <… read more here.
Keywords: fractional laplacian; solutions fractional; multiplicity regularity; laplacian equation ... See more keywords