Partial and full boundary regularity for non-autonomous functionals with Φ-growth conditions
| Autor: | Flavia Giannetti, Atsushi Tachikawa, Antonia Passarelli di Napoli |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Forum Mathematicum. 31:1027-1050 |
| ISSN: | 1435-5337 0933-7741 |
| DOI: | 10.1515/forum-2019-0039 |
| Popis: | We prove partial and full boundary Hölder continuity, under a suitable regularity on the boundary datum, of the minimizers of non-autonomous integral functionals of the type ∫ Ω Φ ( ( A i j α β ( x , u ) D i u α D j u β ) 1 2 ) d x , \int_{\Omega}\Phi\bigl{(}(A^{\alpha\beta}_{ij}(x,u)D_{i}u^{\alpha}D_{j}u^{% \beta})^{\frac{1}{2}}\bigr{)}\mathop{}\!dx, where Ω ⊂ ℝ n {\Omega\subset\mathbb{R}^{n}} is a bounded domain, Φ ( t ) = t p log α ( e + t ) {\Phi(t)=t^{p}\log^{\alpha}(e+t)} with 1 < p ≤ n {1 and α > 0 {\alpha>0} , and A ( x , s ) = ( A i j α β ( x , s ) ) {A(x,s)=(A^{\alpha\beta}_{ij}(x,s))} is a uniformly elliptic, bounded and continuous function. |
| Databáze: | OpenAIRE |
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