Wyniki wyszukiwania

1

Stationary p-harmonic maps into spheres

100%

Strzelecki P.

Banach Center Publications

|

1996

|

tom 33

|

nr 1

383-393

2

Asymptotics for the minimization of a Ginzburg-Landau energy in n dimensions

100%

Strzelecki P.

Colloquium Mathematicum

|

1996

|

tom 70

|

nr 2

271-289

EN

We prove that minimizers $u ∈ W^{1,n}$ of the functional $E_{𝜀}(u) = 1/n ∫_𝛺 |∇u|^{n} dx + 1/(4𝜀^{n}) ∫_𝛺 (1-|u|^{2})^{2} dx$, 𝛺 ⊂ $ℝ^{n}$, n ≥ 3, which satisfy the Dirichlet boundary condition $u_{𝜀} = g$ on 𝜕𝛺 for g:𝜕𝛺 → $S^{n-1}$ with zero topological degree, converge in $W^{1,n}$ and $C^α_{loc}$ for any α<1 - upon passing to a subsequence $𝜀_{k} → 0$ - to some minimizing n-harmonic map. This is a generalization of an earlier result obtained for n=2 by Bethuel, Brezis, and Hélein. An example of nonunique asymptotic behaviour (which cannot occur in two dimensions if deg g = 0) is presented.

3

On the differentiability of solutions of quasilinear elliptic equations

63%

Hajłasz P., Strzelecki P.

Colloquium Mathematicum

|

1993

|

tom 64

|

nr 2

287-291

4

Weak compactness of solutions for fourth order elliptic systems with critical growth

51%

Goldstein P., Strzelecki P., Zatorska-Goldstein A.

Studia Mathematica

|

2013

|

tom 214

|

nr 2

137-156

EN

We consider a class of fourth order elliptic systems which include the Euler-Lagrange equations of biharmonic mappings in dimension 4 and we prove that a weak limit of weak solutions to such systems is again a weak solution to a limit system.

Ograniczanie wyników

2 Colloquium Mathematicum

1 Banach Center Publications

1 Studia Mathematica

4 Strzelecki P.

1 Goldstein P.

1 Hajłasz P.

1 Zatorska-Goldstein A.

1 2013

2 1996

1 1993

Stationary p-harmonic maps into spheres

Asymptotics for the minimization of a Ginzburg-Landau energy in n dimensions

On the differentiability of solutions of quasilinear elliptic equations

Weak compactness of solutions for fourth order elliptic systems with critical growth