Absence of local and global solutions to an elliptic system with time-fractional dynamical boundary conditions.
Absorption effects for some elliptic equations with singularities
We give an expository review of recent results obtained for elliptic equations having natural growth terms of absorption type and singular data. As a new result, we provide an application to the case of lower order terms of subcritical growth, proving a general solvability result with measure data for a class of equations modeled on (1.6).
Almost product structures and Monge-Ampère equations.
Almost-Everywhere Regularity Results for Solutions of Non Linear Elliptic Systems.
𝒞1,β regularity for Dirichlet problems associated to fully nonlinear degenerate elliptic equations
We prove Hölder regularity of the gradient, up to the boundary for solutions of some fully-nonlinear, degenerate elliptic equations, with degeneracy coming from the gradient.
An analytical approach for quasi-linear equation in second order.
An asymmetric Neumann problem with weights
An elliptic equation with no monotonicity condition on the nonlinearity
An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven via variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was obtained using a simple application of topological (Brouwer) degree. Here, a more subtle degree...
An equality for the curvature function of a simple and closed curve on the plane.
An essay on the Interpolation Theorem of Józef Marcinkiewicz - Polish patriot
An example of a nonlinear second order elliptic system in three dimension
We provide an explicit example of a nonlinear second order elliptic system of two equations in three dimension to compare two -regularity theories. We show that, for certain range of parameters, the theory developed in Daněček, Nonlinear Differential Equations Appl.9 (2002), gives a stronger result than the theory introduced in Koshelev, Lecture Notes in Mathematics,1614, 1995. In addition, there is a range of parameters where the first theory gives H"older continuity of solution for all , while...
An example of irregular solution to a nonlinear Euler-Lagrange elliptic system with real analytic coefficients
An existence and localization theorem for the solutions of a Dirichlet problem
We establish an existence theorem for a Dirichlet problem with homogeneous boundary conditions by using a general variational principle of Ricceri.
An existence result for a semipositone problem with a sign changing weight.
An existence result for elliptic problems with singular critical growth.
An existence theorem for a class of elliptic problems in L¹
We prove an existence result for solutions of some class of nonlinear elliptic problems having natural growth terms and L¹ data.
An existence theorem for a strongly nonlinear elliptic problem in Musielak-Orlicz spaces
We prove an existence result for some class of strongly nonlinear elliptic problems in the Musielak-Orlicz spaces , under the assumption that the conjugate function of φ satisfies the Δ₂-condition.
An existence theorem for the Yamabe problem on manifolds with boundary
Let be a compact Riemannian manifold with boundary. We consider the problem (first studied by Escobar in 1992) of finding a conformal metric with constant scalar curvature in the interior and zero mean curvature on the boundary. Using a local test function construction, we are able to settle most cases left open by Escobar’s work. Moreover, we reduce the remaining cases to the positive mass theorem.
An extension of a multiplicity theorem by Ricceri with an application to a class of quasilinear equations
A recent multiplicity result by Ricceri, stated for equations in Hilbert spaces, is extended to a wider class of Banach spaces. Applications to nonlinear boundary value problems involving the p-Laplacian are presented.
An incorrectly posed problem for nonlinear elliptic equations.