On the existence and Hölder regularity of solutions to some nonlinear Cauchy–Neumann problems
On the existence and Hölder regularity of solutions to some nonlinear Cauchy–Neumann problems
复制标题
一些非线性柯西-诺依曼问题解的存在性及其霍尔德正则性
DOI：
10.1007/s00028-023-00899-7
复制
发表时间：
2023
影响因子：
1.4
通讯作者：
A. Audrito
中科院分区：
文献类型：
--
作者：
A. Audrito
We prove uniform parabolic Hölder estimates of De Giorgi–Nash–Moser type for sequences of minimizers of the functionals $$\begin{aligned} {\mathcal {E}}_\varepsilon (W) = \int _0^\infty \frac{e^{- t/\varepsilon }}{\varepsilon } \bigg \{ \int _{\mathbb {R}_+^{N+1}} y^a \left( \varepsilon |\partial _t W|^2 + |\nabla W|^2 \right) \textrm{d}X + \int _{\mathbb {R}^N \times \{0\}} \Phi (w) \,\textrm{d}x\bigg \}\,\textrm{d}t, \qquad \varepsilon \in (0,1) \end{aligned}$$ E ε ( W ) = ∫ 0 ∞ e - t / ε ε { ∫ R + N + 1 y a ε | ∂ t W | 2 + | ∇ W | 2 d X + ∫ R N × { 0 } Φ ( w ) d x } d t , ε ∈ ( 0 , 1 ) where $$a \in (-1,1)$$ a ∈ ( - 1 , 1 ) is a fixed parameter, $$\mathbb {R}_+^{N+1}$$ R + N + 1 is the upper half-space and $$\textrm{d}X = \textrm{d}x \textrm{d}y$$ d X = d x d y . As a consequence, we deduce the existence and Hölder regularity of weak solutions to a class of weighted nonlinear Cauchy–Neumann problems arising in combustion theory and fractional diffusion.
We prove uniform parabolic Hölder estimates of De Giorgi–Nash–Moser type for sequences of minimizers of the functionals $$\begin{aligned} {\mathcal {E}}_\varepsilon (W) = \int _0^\infty \frac{e^{- t/\varepsilon }}{\varepsilon } \bigg \{ \int _{\mathbb {R}_+^{N+1}} y^a \left( \varepsilon |\partial _t W|^2 + |\nabla W|^2 \right) \textrm{d}X + \int _{\mathbb {R}^N \times \{0\}} \Phi (w) \,\textrm{d}x\bigg \}\,\textrm{d}t, \qquad \varepsilon \in (0,1) \end{aligned}$$ E ε ( W ) = ∫ 0 ∞ e - t / ε ε { ∫ R + N + 1 y a ε | ∂ t W | 2 + | ∇ W | 2 d X + ∫ R N × { 0 } Φ ( w ) d x } d t , ε ∈ ( 0 , 1 ) where $$a \in (-1,1)$$ a ∈ ( - 1 , 1 ) is a fixed parameter, $$\mathbb {R}_+^{N+1}$$ R + N + 1 is the upper half-space and $$\textrm{d}X = \textrm{d}x \textrm{d}y$$ d X = d x d y . As a consequence, we deduce the existence and Hölder regularity of weak solutions to a class of weighted nonlinear Cauchy–Neumann problems arising in combustion theory and fractional diffusion.
登录
查看更多内容
简并抛物方程薄障碍问题中的正则自由边界
DOI：
--
发表时间：
2020
期刊：
Algebra i analiz
影响因子：
--
作者：
Banerjee, A.;Danielli, D.;Garofalo, N.;Petrosyan, A.
通讯作者：
Petrosyan, A.
影响因子：
2.4
作者：
Boegelein, Verena;Duzaar, Frank;Marcellini, Paolo
通讯作者：
Marcellini, Paolo
半谐波映射热流的部分正则性及其在自由边界谐波映射中的应用
影响因子：
1.9
作者：
Hyder, Ali;Segatti, Antonio;Sire, Yannick;Wang, Changyou
通讯作者：
Wang, Changyou
简并抛物方程薄障碍问题中奇异集的结构
DOI：
10.1007/s00526-021-01938-2
发表时间：
2021
影响因子：
2.1
作者：
Banerjee, Agnid;Danielli, Donatella;Garofalo, Nicola;Petrosyan, Arshak
通讯作者：
Petrosyan, Arshak