Related papers: Global gradient estimates for a general type of no…
This paper is concerned with global estimates and regularity of solutions for the initial value problem of the retarded parabolic equation $$\frac{\patial u}{\patial t}-\Delta u=f(x,u)+g(u(x,t-r_1(t)),\cdots,u(x,t-r_m(t)))+h(x,t)$$ in a…
The author extends previous results to general classes of equations under weaker assumptions obtained in 2016 by Bao, Dong and Jiao concerning the study of the regularity of solutions for the first initial-boundary value problem for…
We derive logarithmic gradient estimate and universal boundedness estimate for semilinear elliptic equations on \RCD\, metric measure spaces, which contains the class of Riemannian manifolds with Ricci curvature bounded below. These…
We propose the first global accelerated gradient method for Riemannian manifolds. Toward establishing our result we revisit Nesterov's estimate sequence technique and develop an alternative analysis for it that may also be of independent…
In this article, by applying the well known method for dealing with $p$-Laplace type elliptic boundary value problems, the authors establish a sharp estimate for the decreasing rearrangement of the gradient of solutions to the Dirichlet and…
We provide sparse estimates for gradients of solutions to divergence form elliptic partial differential equations in terms of the source data. We give a general result of Meyers (or Gehring) type, a result for linear equations with VMO…
We establish H\"older estimates for the time derivative of solutions of non-local parabolic equations under mild assumptions for the boundary data. As a consequence we are able to extend the Evans-Krylov estimate for rough kernels to…
We prove global Holder estimates for solution of fully nonlinear elliptic or degenerate elliptic equations in unbounded domains under geometric conditions on the domain a' la Cabre'.
In this paper, we prove Souplet-Zhang type gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces with the compact boundary under the Dirichlet boundary condition when the Bakry-Emery Ricci tensor and the…
We consider singular perturbations of eigenvalue problems. We prove that to these problems correspond simple eigenvalues and we study their asymptotic behavior. As a result, we prove global bifurcation results for non uniformly and fully…
A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…
We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the…
This paper is focused on the generalized Forchheimer flows of slightly compressible fluids in porous media. They are reformulated as a degenerate parabolic equation for the pressure. The initial boundary value problem is studied with…
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…
In historical mathematics and physics, the Kardar-Parisi-Zhang equation or a quasilinear stationary version of a time-dependent viscous Hamilton-Jacobi equation in growing interface and universality classes, is also known by the different…
In this paper, first we study carefully the positive solutions to $\Delta u+\lambda_{1}u\ln u +\lambda_{2}u^{b+1}=0$ defined on a complete noncompact Riemannian manifold $(M, g)$ with $Ric(g)\geq -Kg$, which can be regarded as…
We derive localized and global noncompact versions of Hamilton's gradient estimate for positive solutions to the heat equation on Riemannian manifolds with Ricci curvature bounded below. Our estimates are essentially optimal and…
In this paper, we prove global gradient estimates for solutions to linear elliptic and parabolic equations. For a sufficiently smooth bounded convex domain $\Omega \subset \mathbb{R}^N$, we show that a solution $\phi \in…
This paper is a contribution to the study of regularity theory for nonlinear elliptic equations. The aim of this paper is to establish some global estimates for non-uniformly elliptic in divergence form as follows \begin{align*}…
Using the rudiments of pde jets theory in a nonstandard setting, we first deepen and extend previous nonstandard existence results for generalized solutions of linear differential equations and second extend the previous results for linear…