Neumann problem in a class of harmonic functions in domains with a piecewise-Lyapunov boundary.
Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces
We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space.
Neumann-Neumann algorithms for spectral elements in three dimensions
Neumann-Neumann methods for vector field problems.
New a priori estimates for -nonlinear elliptic systems with strong nonlinearities in the gradient, .
New and old function spaces in the theory of PDEs and nonlinear analysis
New estimates for div-curl products and very weak solutions of PDEs
New estimates for elliptic equations and Hodge type systems
We establish new estimates for the Laplacian, the div-curl system, and more general Hodge systems in arbitrary dimension , with data in . We also present related results concerning differential forms with coefficients in the limiting Sobolev space .
New exact solutions to the nonautonomous Liouville equation.
New ideas on complete integrability
New isoperimetric estimates for solutions to Monge-Ampère equations
New linking theorems
New Liouville theorems for linear second order degenerate elliptic equations in divergence form
New mixed finite volume methods for second order eliptic problems
In this paper we introduce and analyze new mixed finite volume methods for second order elliptic problems which are based on H(div)-conforming approximations for the vector variable and discontinuous approximations for the scalar variable. The discretization is fulfilled by combining the ideas of the traditional finite volume box method and the local discontinuous Galerkin method. We propose two different types of methods, called Methods I and II, and show that they have distinct advantages over...
New nonlinear Picone identities with variable exponents and applications
This paper introduces two novel nonlinear anisotropic Picone identities with variable exponents that expand upon the traditional identity used for the ordinary Laplace equation. Additionally, the research explores potential applications of these findings in anisotropic Sobolev spaces featuring variable exponents.
New optimal regularity results for infinite-dimensional elliptic equations
In questo articolo si ottengono stime di Schauder di tipo nuovo per equazioni ellittiche infinito-dimensionali del secondo ordine con coefficienti Hölderiani a valori nello spazio degli operatori Hilbert-Schmidt. In particolare si mostra che la derivata seconda delle soluzioni è Hilbert-Schmidt.
New regularity results for a generic model equation in exterior 3D domains
We consider a generic scalar model for the Oseen equations in an exterior three-dimensional domain. We assume the case of a non-constant coefficient function. Using a variational approach we prove new regularity properties of a weak solution whose existence and uniqueness in anisotropically weighted Sobolev spaces were proved in [10]. Because we use some facts and technical tools proved in the above mentioned paper, we give also a brief review of its results and methods.
New results concerning the DWR method for some nonconforming FEM
This paper presents a unified framework for the dual-weighted residual (DWR) method for a class of nonconforming FEM. Our approach is based on a modification of the dual problem and uses various ideas from literature which are combined in a new manner. The results are new error identities for some nonconforming FEM. Additionally, a posteriori error estimates with respect to the discrete -seminorm are derived.
New results on the Burgers and the linear heat equations in unbounded domains.
We consider the Burgers equation and prove a property which seems to have been unobserved until now: there is no limitation on the growth of the nonnegative initial datum u0(x) at infinity when the problem is formulated on unbounded intervals, as, e.g. (0 +∞), and the solution is unique without prescribing its behaviour at infinity. We also consider the associate stationary problem. Finally, some applications to the linear heat equation with boundary conditions of Robin type are also given.
New solutions of equations on