Existence and regularity of solutions of some elliptic system in domains with edges
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# Existence and regularity of solutions of some elliptic system in domains with edges by Wojciech M. ZajaМЁczkowski

• ·

Written in English

### Subjects:

• Differential equations, Elliptic.

## Book details:

Edition Notes

Classifications The Physical Object Statement Wojciech M. Zajączkowski. Series Dissertationes mathematicae,, Rozprawy matematyczne ;, 274, Rozprawy matematyczne ;, 274. LC Classifications QA1 .D54 no. 274, QA377 .D54 no. 274 Pagination 95 p. ; Number of Pages 95 Open Library OL2260744M ISBN 10 8301087676 LC Control Number 89142401

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Abstract In this paper, we study the existence and regularity of positive solution for an elliptic system on a bounded and regular domain. The non linearities in this equation are functions of. In this paper, we study the existence and regularity of positive solu-tion for an elliptic system on a bounded and regular domain. The non linearities in this equation are functions of Caratheodory type satisfying some exponential growth conditions. 1 Introduction In this work, we study the elliptic system −∆ pu= f(x,u,v) in Ω −∆ pv= g(x,u,v) in Ω.   Existence and regularity of positive solutions of a degenerate elliptic Dirichlet problem of the form in Ω, on, where Ω is a bounded smooth domain in,, are obtained via new embeddings of some weighted Sobolev spaces with singular weights is seen that and admit many singular points in Ω. The main embedding results in this paper provide some generalizations of the well‐known Cited by: 1. This paper is a sketch of the theory of general elliptic boundary value problems in domains with edges of various dimensions on the boundary. In particular, the class of admissible domains contains polygons, cones, lenses and polyhedrons. Discontinuities .

Elliptic Boundary Value Problems on Corner Domains: Smoothness and Asymptotics of Solutions Monique Dauge (auth.) This research monograph focusses on a large class of variational elliptic problems with mixed boundary conditions on domains with various corner singularities, edges, polyhedral vertices, cracks, slits. Nonlinear elliptic singular boundary value problems have been studied during the last forty years in what concerns existence, uniqueness (or multiplicity) and regularity of positive solutions. The rst relevant existence results for a class of problems including the model case () with psmooth and >0, were obtained in two important papers by. Our aim here is to illustrate some of the relevant ideas in the theory of Elliptic systems: existence of weak solutions 53 the theory of elliptic regularity: the Dirichlet problem for the Laplace operator. Introduction. 6 Regularity up to the boundary 45 7 Interior regularity for nonlinear problems 49 8 H¨older, Morrey and Campanato spaces 51 9 XIX Hilbert problem and its solution in the two-dimensional case 57 10 Schauder theory 61 11 Regularity in Lp spaces 65 ⇤PhD course given in and then in , , lectures typed by to and.

the regularity of solutions of boundary value problems for linear elliptic systems on smooth domains in Holder and Sobolev spaces. Around the same time, analytic regu-¨ larity was proved by Morrey and Nirenberg [70]. There exist many books presenting this basic elliptic theory, some of them focussing on the fundamental theory of linear ellip-. () Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ 3. Part II: Regularity in neighbourhoods of edges. Proceedings of the Royal Society of Edinburgh: Section A Mathematics , is shown to be a well-posed problem under some sign and growth restrictions off and its partial derivatives. It can be seen as an initial value problem, with initial valueϕ, in the spaceC 0 0 $$(\overline {\Omega '})$$ and satisfying the strong order-preserving property. In the case thata ij andf do not depend onx 0 or are periodic inx 0, it is shown that the corresponding dynamical system. of weak solution, needed to have a well deﬁned integral in (), is an additional diﬃculty. Notice that such a request is a priori assumed in some regularity results under the p,q-growth, see for example Leonetti [22], Bildhauer–Fuchs [1] and Cupini– Marcellini–Mascolo [10]. In this paper we prove the existence of a weak solution u.