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Boundary regularity of flows under perfect slip boundary conditions

Petr Kaplický, Jakub Tichý (2013)

Open Mathematics

We investigate boundary regularity of solutions of generalized Stokes equations. The problem is complemented with perfect slip boundary conditions and we assume that the nonlinear elliptic operator satisfies non-standard ϕ-growth conditions. We show the existence of second derivatives of velocity and their optimal regularity.

Boundary singularities of solutions to quasilinear elliptic equations

Vladimir Kozlov, Vladimir Maz'ya (1999)

Journées équations aux dérivées partielles

Asymptotic formulae for solutions to boundary value problems for linear and quasilinear elliptic equations and systems near a boundary point are discussed. The boundary is not necessarily smooth. The main ingredient of the proof is a spectral splitting and reduction of the original problem to a finite-dimensional dynamical system. The linear version of the corresponding abstract asymptotic theory is presented in our new book “Differential equations with operator coefficients”, Springer, 1999.

Boundary trace of positive solutions of nonlinear elliptic inequalities

Moshe Marcus, Laurent Véron (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We develop a new method for proving the existence of a boundary trace, in the class of Borel measures, of nonnegative solutions of - Δ u + g ( x , u ) ≥ 0 in a smooth domain Ω under very general assumptions on g . This new definition which extends the previous notions of boundary trace is based upon a sweeping technique by solutions of Dirichlet problems with measure boundary data. We also prove a boundary pointwise blow-up estimate of any solution of such inequalities in terms of the Poisson kernel. If the nonlinearity...

Boundary trace of solutions of semilinear elliptic equalities and inequalities

Laurent Véron (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The boundary trace problem for positive solutions of - △ ⁢ u + g ⁢ x , u ≥ 0 is considered for nonlinearities of absorption type, and three different methods for defining the trace are compared. The boundary trace is obtained as a generalized Borel measure. The associated Dirichlet problem with boundary data in the set of such Borel measures is studied.

Boundary value problems and layer potentials on manifolds with cylindrical ends

Marius Mitrea, Victor Nistor (2007)

Czechoslovak Mathematical Journal

We study the method of layer potentials for manifolds with boundary and cylindrical ends. The fact that the boundary is non-compact prevents us from using the standard characterization of Fredholm or compact pseudo-differential operators between Sobolev spaces, as, for example, in the works of Fabes-Jodeit-Lewis and Kral-Wedland . We first study the layer potentials depending on a parameter on compact manifolds. This then yields the invertibility of the relevant boundary integral operators in the...

Boundary value problems for elliptic equations.

Carlos E. Kenig (1991)

Publicacions Matemàtiques

In this note I will describe some recent results, obtained jointly with R. Fefferman and J. Pipher [RF-K-P], on the Dirichlet problem for second-order, divergence form elliptic equations, and some work in progress with J. Pipher [K-P] on the corresponding results for the Neumann and regularity problems.

Currently displaying 81 – 100 of 132