# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
The asymptotics of the solutions of linear elliptic variational problems in domains with edges. (English) Zbl 0725.49002

Summary: Let G be a bounded domain in ${ℝ}^{n}$ with piecewise smooth boundary

$\partial G={\cup }_{j=1}^{T}{{\Gamma }}_{j}\cap {\cup }_{j=1}^{T-1}{ℳ}_{j},$

where ${{\Gamma }}_{j}$ and ${ℳ}_{j}$ are smooth connected (n-1)- and (n-2)-dimensional manifolds, respectively. Furthermore, let L be an elliptic differential operator of order 2m, a(u,v) a Dirichlet form corresponding to L and ${𝒱}^{m}\left(G\right)$ the space of all functions from ${W}_{2}^{m}\left(G\right)$ satisfying the stable boundary conditions ${B}_{k}^{\left(j\right)}u=0$ on ${{\Gamma }}_{j}$ and ${N}_{k}^{\left(j\right)}u=0$ on ${ℳ}_{j}$ (ord ${B}_{k}^{\left(j\right)}\le m-1$ and ord ${N}_{k}^{\left(j\right)}\le m-2\right)$. It is proved that the solution $u\in {𝒱}^{m}\left(G\right)$ of the variational problem $a\left(u,v\right)=$ for all $v\in {𝒱}^{m}\left(G\right)$ under certain conditions on f can be written as a sum of some singular terms and a regular term ${u}_{1}\in {W}_{2}^{m+\beta }\left(G\right)$ ($\beta \in \left(0,1\right]\right)$.

##### MSC:
 49J20 Optimal control problems with PDE (existence) 35J40 Higher order elliptic equations, boundary value problems 35J50 Systems of elliptic equations, variational methods