By means of the modified method test functions, we obtain sufficient conditions absence nontrivial solutions for some classes semilinear elliptic inequalities higher order and quasilinear containing nonhomogeneous terms (independent unknown function).

We show that bounded solutions of the quasilinear elliptic equation \(\Delta_{p(x)} u=g+div(\textbf{F})\) are locally Hölder continuous provided functions \(g\) and \(\textbf{F}\) in suitable Lebesgue spaces.

We study linear and quasilinear Venttsel boundary value problems involving elliptic operators with discontinuous coefficients. On the basis of a priori estimates obtained, maximal regularity strong solvability in Sobolev spaces are proved.

We establish pointwise andW−1 ∞ estimates for finite element methods for a class of second-order quasilinear elliptic problems defined on domains Ω in Rn. These estimates are localized in that they indicate that the pointwise dependence of the error on global norms of the solution is of higher order. Our pointwise estimates are similar to and rely on results and analysis techniques of Schatz fo...

We consider convex level sets of solutions a class quasilinear elliptic equations. prove weak Harnack inequality for the eigenvalues Weingarten tensor and then obtain quantitative version constant rank theorem.

Based on the analysis of Cockburn et. al. [Math. Comp. 78 (2009), pp. 1-24] for a selfadjoint linear elliptic equation, we first discuss superconvergence results for nonselfadjoint linear elliptic problems using discontinuous Galerkin methods. Further, we have extended our analysis to derive superconvergence results for quasilinear elliptic problems. When piecewise polynomials of degree k ≥ 1 a...

We prove an existence result for the Dirichlet problem associated to some degenerate quasilinear elliptic equations in a bounded open set Ω in R in the setting of weighted Sobolev spaces W 1,p 0 (Ω, ω). 2000 Mathematics Subject Classification: 35J70, 35J60.

We study a boundary-value quasilinear elliptic problem on a generic time scale. Making use of the fixed-point index theory, sufficient conditions are given to obtain existence, multiplicity, and infinite solvability of positive solutions. AMS Subject Classification: 34B18, 39A10, 93C70.

Under suitable assumptions we prove, via the Leray-Schauder fixed point theorem, the existence of a solution for quasilinear elliptic boundary value problem in C(Ω̄) ∩ W (Ω), q > N which satisfies in addition the condition, (1+ | x |) 1 2u ∈ C(Ω̄).