On elliptic equations in a half space or in convex wedges with irregular coefficients
@article{Dong2013OnEE, title={On elliptic equations in a half space or in convex wedges with irregular coefficients}, author={Hongjie Dong}, journal={Advances in Mathematics}, year={2013}, volume={238}, pages={24-49} }
5 Citations
On the impossibility of $W_p^2$ estimates for elliptic equations with piecewise constant coefficients
- Mathematics
- 2014
Parabolic Equations in Simple Convex Polytopes with Time Irregular Coefficients
- MathematicsSIAM J. Math. Anal.
- 2014
It is proved the W 1,2 p-estimate and solvability for the Dirichlet problem of second-order parabolic equations in simple convex polytopes with time irregular coefficients when p is in (1,2) when the coefficients are unknown.
Gradient Estimates for Parabolic and Elliptic Systems from Linear Laminates
- Mathematics
- 2012
We establish several gradient estimates for second-order divergence type parabolic and elliptic systems. The coefficients and data are assumed to be Hölder or Dini continuous in the time variable and…
Boundary Gradient Estimates for Parabolic and Elliptic Systems from Linear Laminates
- Mathematics
- 2013
We study boundary gradient estimates for second-order divergence type parabolic and elliptic systems in $C^{1,\alpha}$ domains. The coefficients and data are assumed to be H\"older in the time…
Compressible Navier–Stokes–Fourier flows at steady-state
- MathematicsSão Paulo Journal of Mathematical Sciences
- 2021
The heat conducting compressible viscous flows are governed by the Navier-Stokes-Fourier (NSF) system. In this paper, we study the NSF system accomplished by the Newton law of cooling for the heat…
References
SHOWING 1-10 OF 49 REFERENCES
Second-order eliptic and parabolic equations with B (r2, V MO) coefficients
- Mathematics
- 2010
The solvability in Sobolev spaces W 1,2 p is proved for nondivergence form second-order parabolic equations for p > 2 close to 2. The leading coefficients are assumed to be measurable in the time…
On linear and nonlinear elliptic boundary value problems in the plane with discontinuous coefficients
- Mathematics
- 2011
Global Holder regularity of the gradient in Morrey spaces
is established for planar elliptic discontinuous equations,
estimating in an explicit way the Holder exponent in terms of the
eigenvalues…
ON EQUATIONS OF MINIMAX TYPE IN THE THEORY OF ELLIPTIC AND PARABOLIC EQUATIONS IN THE PLANE
- Mathematics
- 1970
The existence and uniqueness of the solution in Sobolev spaces () is proved for the first boundary value problem for elliptic (parabolic) equations of the form Here and in the elliptic case, in the…
Boundary Layers on Sobolev–Besov Spaces and Poisson's Equation for the Laplacian in Lipschitz Domains
- Mathematics
- 1998
We study inhomogeneous boundary value problems for the Laplacian in arbitrary Lipschitz domains with data in Sobolev–Besov spaces. As such, this is a natural continuation of work in [Jerison and…
Elliptic Equations in Polyhedral Domains
- Mathematics
- 2010
This is the first monograph which systematically treats elliptic boundary value problems in domains of polyhedral type. The authors mainly describe their own recent results focusing on the Dirichlet…
Lp-Estimates for a Solution to the Dirichlet Problem and to the Neumann Problem for the Heat Equation in a Wedge with Edge of Arbitrary Codimension
- Mathematics
- 2001
The Dirichlet problem and the Neumann problem in a wedge with edge of an arbitrary codimension are studied. On the basis of the Green functions of these problems in a cone, estimates for solutions…
^{2,}-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients
- Mathematics
- 1993
We prove a well-posedness result in the class W 2,p ∩ W 0 1,p for the Dirichlet problem Lu = f a.e. in Ω, u = 0 on ∂Ω. We assume the coefficients of the elliptic nondivergence form equation that we…
Solvability of second-order equations with hierarchically partially BMO coefficients
- Mathematics
- 2012
By using some recent results for divergence form equations, we study the $L_p$-solvability of second-order elliptic and parabolic equations in nondivergence form for any $p\in (1,\infty)$. The…