相关论文: On solutions of elliptic equations with variable e…
The Dirichlet problem in arbitrary domains for a wide class of anisotropic elliptic equations of the second order with variable exponent nonlinearities and the right-hand side as a measure is considered. The existence of an entropy solution…
We study nonlinear measure data elliptic problems involving the operator exposing generalized Orlicz growth. Our framework embraces reflexive Orlicz spaces, as well as natural variants of variable exponent and double-phase spaces.…
The solvability in Sobolev spaces is proved for divergence form second order elliptic equations in the whole space, a half space, and a bounded Lipschitz domain. For equations in the whole space or a half space, the leading coefficients…
We study the well-posedness of solutions to the general nonlinear parabolic equations with merely integrable data in time-dependent Musielak-Orlicz spaces. With the help of a density argument, we establish the existence and uniqueness of…
Boundary value problems for a class of quasilinear elliptic equations, with an Orlicz type growth and L^1 right-hand side are considered. Both Dirichlet and Neumann problems are contemplated. Existence and uniqueness of generalized…
Consider positive solutions to second order elliptic equations with measurable coefficients in a bounded domain, which vanish on a portion of the boundary. We give simple necessary and sufficient geometric conditions on the domain, which…
The solvability in $W^{2}_{p}(\bR^{d})$ spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the…
We consider nonlinear elliptic inclusion having a measure in the right-hand side of the type $\beta(u)-div a(x,Du)\ni \mu$ in $\Omega$ a bounded domain in $\mathbb{R}^{N},$ with $\beta$ is a maximal monotone graph in $\mathbb{R}^2$ 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…
In this article, we consider a higher-order elliptic equation with nonsmooth coefficients with respect to Orlicz spaces on the domain $\Omega\subset\mathbb{R}^{n}$. The separable subspace of this space is distinguished in which infinitely…
In this paper we prove the existence of a nontrivial non-negative radial solution for a quasilinear elliptic problem. Our aim is to approach the problem variationally by using the tools of critical points theory in an Orlicz-Sobolev space.…
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…
Anisotropic exponential cosmological solutions for a space of arbitrary dimension filled with ordinary matter in the 4th and 5th orders of Lovelock gravity are obtained. Also we have supposed a generalization of such solutions on an…
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…
We establish the solvability of second order divergence type parabolic systems in Sobolev spaces. The leading coefficients are assumed to be only measurable in one spatial direction on each small parabolic cylinder with the spatial…
We propose a probabilistic definition of solutions of semilinear elliptic equations with (possibly nonlocal) operators associated with regular Dirichlet forms and with measure data. Using the theory of backward stochastic differential…
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 variable and two coordinates of space…
In this paper, we study a second-order, nonlinear evolution equation with damping arising in elastodynamics. The nonlinear term is monotone and possesses a convex potential but exhibits anisotropic and nonpolynomial growth. The appropriate…
In this article we give an extention of the L^2-theory of anisotropic singular perturbations for elliptic problems. We study a linear and some nonlinear problems involving L^p data (1<p<2). Convergences in pseudo Sobolev spaces are proved…
We characterize, in the terms of intrinsic Hausdorff measures, the size of~removable sets for H\"older continuous solutions to elliptic equations with Musielak-Orlicz growth. In the general case we provide an elegant form of the measure…