Semilinear elliptic systems with measure data
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 605495971 | ||
| 003 | CHVBK | ||
| 005 | 20210128100534.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10231-013-0364-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-013-0364-4 | ||
| 100 | 1 | |a Klimsiak |D Tomasz |u Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100, Toruń, Poland |4 aut | |
| 245 | 1 | 0 | |a Semilinear elliptic systems with measure data |h [Elektronische Daten] |c [Tomasz Klimsiak] |
| 520 | 3 | |a We study the Dirichlet problem for systems of the form $$-\varDelta u^k=f^k(x,u)+\mu ^k,\,x\in \varOmega ,\,k=1,\ldots ,n$$ - Δ u k = f k ( x , u ) + μ k , x ∈ Ω , k = 1 , ... , n , where $$\varOmega \subset \mathbb{R }^d$$ Ω ⊂ R d is an open (possibly nonregular) bounded set, $$\mu ^1,\ldots ,\mu ^n$$ μ 1 , ... , μ n are bounded diffuse measures on $$\varOmega ,\,f=(f^1,\ldots ,f^n)$$ Ω , f = ( f 1 , ... , f n ) satisfies some mild integrability condition and the so-called angle condition. Using the methods of probabilistic Dirichlet forms theory, we show that the system has a unique solution in the generalized Sobolev space $$\dot{H}^{1}_\mathrm{loc}(\varOmega )$$ H ˙ loc 1 ( Ω ) of functions having fine gradient. We also provide a stochastic representation of the solution. | |
| 540 | |a The Author(s), 2013 | ||
| 690 | 7 | |a Semilinear elliptic systems |2 nationallicence | |
| 690 | 7 | |a Laplacian |2 nationallicence | |
| 690 | 7 | |a Dirichlet problem |2 nationallicence | |
| 690 | 7 | |a Measure data |2 nationallicence | |
| 690 | 7 | |a Dirichlet form |2 nationallicence | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/1(2015-02-01), 55-76 |x 0373-3114 |q 194:1<55 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-013-0364-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-013-0364-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Klimsiak |D Tomasz |u Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100, Toruń, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/1(2015-02-01), 55-76 |x 0373-3114 |q 194:1<55 |1 2015 |2 194 |o 10231 | ||