Related papers: Regularity for quasilinear vectorial elliptic syst…
We study iterative finite element approximations for the numerical approximation of semilinear elliptic boundary value problems with monotone nonlinear reactions of subcritical growth. The focus of our contribution is on an optimal a priori…
We show that the new result on H\"older continuity of solutions to a class of nondiagonal elliptic systems with $p$-growth in [2] can be used to improve the $L^q$ theory for such systems.
Variational regularization and the quasisolutions method are justified for unbounded closed, possibly nonlinear, operators. The argument is quite simple and yields general results.
We establish a general theorem improving regularity of solutions of elliptic pseudodifferential equations. It allows to resolve in a unified way the regularity issue for a broad class of nonlinear elliptic equations and systems appearing in…
By virtue of a weak comparison principle in small domains we prove axial symmetry in convex and symmetric smooth bounded domains as well as radial symmetry in balls for regular solutions of a class of quasi-linear elliptic systems in…
We investigate the iterative methods proposed by Maz'ya and Kozlov (see [KM1], [KM2]) for solving ill-posed inverse problems modeled by partial differential equations. We consider linear evolutionary problems of elliptic, hyperbolic and…
We study the uniqueness problem of $\sigma$-regular solution of the equation, $$-\Delta_p u+ \abs u^{q-1}u =h \quad on\quad \RN, $$ where $q>p-1>0.$ and $N> p.$ Other coercive type equations associated to more general differential operators…
We prove the interior and global Lipschitz regularity results for a solution of fully nonlinear equations with $(p,q)$-growth. We prove that for a small gap $q-p$, a solution is locally or globally Lipschitz continuous. We also prove that a…
We announce some new results for proving H\"older continuity of weak solutions to quasilinear parabolic equations whose prototype takes the form $$u_t - div (|\nabla u|^{p-2}\nabla u)= 0 \qquad \text{or} \qquad u_t - div…
We study finite energy solutions to quasilinear elliptic equations of the type $$ -\Delta_pu=\sigma \, u^q \quad \text{in } \mathbb{R}^n,$$ where $\Delta_p$ is the $p$-Laplacian, $p>1$, and $\sigma$ is a nonnegative function (or measure) on…
It is shown by means of reiterated two-scale convergence in the Sobolev-Orlicz setting, that the sequence of solutions of a class of highly oscillatory problems involving nonlinear elliptic operators with nonstandard growth, converges to a…
A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…
In this work, we are interested in to study removability of a singular set in the boundary for some classes of quasilinear elliptic equations. We will approach this question in two different ways: through an asymptotic behavior at the…
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…
We obtain existence and global regularity estimates for gradients of solutions to quasilinear elliptic equations with measure data whose prototypes are of the form $-{\rm div} (|\nabla u|^{p-2} \nabla u)= \delta\, |\nabla u|^q +\mu$ in a…
We study partial regularity for degenerate elliptic systems of double-phase type, where the growth function is given by $H(x,t)=t^p+a(x)t^q$ with $1<p\leq q$ and $a(x)$ a nonnegative $C^{0,\alpha}$-continuous function. Our main result…
In this paper, we investigate the existence of solutions for a class of quasilinear elliptic system \begin{eqnarray*} \begin{cases}{ccc} -\mbox{div}(\phi_1(|\nabla u|)\nabla u)+V_1(x)\phi_1(|u|)u=\lambda F_u(x, u,v), \ \ x\in \mathbb R^N,…
We use an iteration procedure propped up by a a classical form of the maximum principle to show the existence of solutions to a nonlinear Poisson equation with Dirichlet boundary conditions. These methods can be applied to the case of…
A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. Exponential splines are used…
In this paper we consider positive solutions to quasilinear elliptic problem with singular nonlinearities. We provide a H\"{o}pf type boundary lemma via a suitable scaling argument that allows to deal with the lack of regularity of the…