相关论文: On the existence of $W^{2}_{p}$ solutions for full…

We study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient, whose model is $$ \begin{cases} -\Delta u +…

Investigating for interior regularity of viscosity solutions to the fully nonlinear elliptic equation $$F(x,u,\triangledown u,\triangledown ^2 u)=0,$$ we establish the interior $C^{1+1}$ continuity under the assumptions that $F$ is…

Optimal second-order regularity in the space variables is established for solutions to Cauchy-Dirichlet problems for nonlinear parabolic equations and systems of $p$-Laplacian type, with square-integrable right-hand sides and initial data…

We consider stable solutions of a semilinear elliptic equation with homogeneous Neumann boundary conditions. A classical result of Casten, Holland [20] and Matano [44] states that all stable solutions are constant in convex bounded domains.…

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 leading coefficients are assumed to be in…

We study the critical points of the solution of second elliptic equations in divergence and diagonal form with a bounded and positive definite coefficient, under the assumption that the statement of the Hopf lemma holds (sign assumptions on…

We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…

We study a class of nonlinear elliptic problems with Dirichlet conditions in the framework of the Sobolev anisotropic spaces with variable exponent, involving an anisotropic operator on an unbounded domain $\Omega\subset \>I\!\!R^{N}\>(N…

We obtain local pointwise second derivative estimates for $W^{2,p}$-strong solutions to a class of fully nonlinear elliptic equations on Euclidean domains, motivated by problems in conformal geometry.

We prove the existence of solutions for some integro-differential systems containing equations with and without the drift terms in the H^2 spaces by virtue of the fixed point technique when the elliptic equations contain second order…

We deals with nonlinear elliptic Dirichlet problems of the form $${\rm div}(|D u|^{p-2}D u )+f(u)=0\quad\mbox{ in }\Omega,\qquad u\in H^{1,p}_0(\Omega) $$ where $\Omega$ is a bounded domain in $\mathbb{R}^n$, $n\ge 2$, $p> 1$ and $f$ has…

We establish the existence of a solution to the Navier-Stokes equations on a moving domain with surface tension in an optimal Sobolev space for the case of two space dimension. No compatibility conditions are required to guarantee the…

We prove the unique solvability of second order elliptic equations in non-divergence form in Sobolev spaces. The coefficients of the second order terms are measurable in one variable and VMO in other variables. From this result, we obtain…

We consider uniformly elliptic and parabolic second-order equations with bounded zeroth-order and bounded VMO leading coefficients and possibly growing first-order coefficients. We look for solutions which are summable to the $p$-th power…

The purpose of this paper is to prove some existence and non-existence theorems for the nonlinear elliptic problems of the form -{\Delta}_{p}u={\lambda}k(x)u^{q}\pmh(x)u^{{\sigma}} if x\in{\Omega}, subject to the Dirichlet conditions…

We prove weighted and mixed-norm Sobolev estimates for fully nonlinear elliptic and parabolic equations in the whole space under a relaxed convexity condition with almost VMO dependence on space-time variables. The corresponding interior…

We derive global gradient estimates for $W^{1,p}_0(\Omega)$-weak solutions to quasilinear elliptic equations of the form $$ \mathrm{div\,}\mathbf{a}(x,u,Du)=\mathrm{div\,}(|F|^{p-2}F) $$ over $n$-dimensional Reifenberg flat domains. The…

We are concerned with the solvability of linear second order elliptic partial differential equations with nonlinear boundary conditions at resonance, in which the nonlinear boundary conditions perturbation is not necessarily required to…

This paper proves the existence of nontrivial solution for two classes of quasilinear systems of the type \begin{equation*} \left\{\; \begin{aligned} -\Delta_{\Phi_{1}} u&=F_u(x,u,v)+\lambda R_u(x,u,v)\;\text{ in } \Omega& \\…

We prove that second order linear operators on $\mathbb{R}^{n+m}$ of the form $L(x,y,D_x,D_y) = L_1(x,D_x) + g(x) L_2(y,D_y)$, where $L_1$ and $L_2$ satisfy Morimoto's super-logarithmic estimates and $g$ is smooth, nonnegative, and vanishes…