Results 1 to 10 of about 148 (25)
Fractional double phase Robin problem involving variable order-exponents and Logarithm-type nonlinearity [PDF]
, 2022 In this paper, we study the existence of solutions for the new fractinal Robin equations with variable exponents. Moreover, we deal with the logarithm-type nonlinearity. In particular, we consider two cases: critical and subcritical cases.
arxiv +1 more source
On discrete boundary value problems with nonlocal conditions in a quarter-plane [PDF]
arXiv, 2023 We consider discrete analogue of model pseudo-differential equations in discrete plane sector using discrete variant of Sobolev--Slobodetskii spaces. Starting from the concept of wave factorization for elliptic periodic symbol we describe solvability conditions for the equations and corresponding discrete boundary value problems.
arxiv
On a general discrete boundary value problem [PDF]
arXiv, 2023 We study a general discrete boundary value problem in Sobolev--Slobodetskii spaces in a plane quadrant and reduce it to a system of integral equations. We show a solvability of the system for a small size of discreteness starting from a solvability of its continuous analogue.
arxiv
Realizations of Differential Operators on Conic Manifolds with Boundary [PDF]
Ann. Global Anal. Geom. 31, 223-285 (2007), 2004 We study the closed extensions (realizations) of differential operators subject to homogeneous boundary conditions on weighted L_p-Sobolev spaces over a manifold with boundary and conical singularities. Under natural ellipticity conditions we determine the domains of the minimal and the maximal extension.
arxiv +1 more source
Asymptotically linear magnetic fractional problems [PDF]
arXiv, 2023 The aim of this paper is investigating the existence and multiplicity of weak solutions to non--local equations involving the {\em magnetic fractional Laplacian}, when the nonlinearity is subcritical and asymptotically linear at infinity. We prove existence and multiplicity results by using variational tools, extending to the magnetic local and non ...
arxiv
Boundary value problems of elliptic operators and reduction to the boundary techniques [PDF]
, 2018 We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.
arxiv +1 more source
Maximal $L_p$-regularity of non-local boundary value problems [PDF]
Monatsh. Math. 176 (2015), 53-80, 2014 We investigate the $\mathcal R$-boundedness of operator families belonging to the Boutet de Monvel calculus. In particular, we show that weakly and strongly parameter-dependent Green operators of nonpositive order are $\mathcal R$-bounded. Such operators appear as resolvents of non-local (pseudodifferential) boundary value problems.
arxiv +1 more source
On Kac's principle of not feeling the boundary for the Kohn Laplacian on the Heisenberg group [PDF]
Proc. Amer. Math. Soc., 144 (2016), 709-721, 2015 In this note we construct an integral boundary condition for the Kohn Laplacian in a given domain on the Heisenberg group extending to the setting of the Heisenberg group M. Kac's "principle of not feeling the boundary". This also amounts to finding the trace on smooth surfaces of the Newton potential associated to the Kohn Laplacian.
arxiv +1 more source
On the stabilization of the elasticity system by the boundary [PDF]
arXiv, 2007 We obtain free of resonances regions for the elasticity system in the exterior of a strictly convex body with dissipative boundary conditions under some natural assumptions on the behaviour of the geodesics on the boundary.
arxiv
Potentials for elliptic boundary value problems in cones [PDF]
arXiv, 2014 We consider an elliptic pseudo differential equation in a multi-dimensional cone and starting wave factorization concept we add some boundary conditions. For the simplest cases explicit formulas for solution are given like layer potentials for classical case.
arxiv