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pro vyhledávání: '"MacDonald, Sullivan Francis"'
Autor:
MacDonald, Sullivan Francis
We investigate the number of half-regular squares required to decompose a non-negative $C^{k,\alpha}(\mathbb{R}^n)$ function into a sum of squares. Each non-negative $C^{3,1}(\mathbb{R}^n)$ function is known to be a finite SOS in $C^{1,1}(\mathbb{R}^
Externí odkaz:
http://arxiv.org/abs/2309.07275
Autor:
MacDonald, Sullivan Francis
This work showcases level set estimates for weak solutions to the $p$-Poisson equation on a bounded domain, which we use to establish Lebesgue space inclusions for weak solutions. In particular we show that if $\Omega\subset\mathbb{R}^n$ is a bounded
Externí odkaz:
http://arxiv.org/abs/2309.07274
Autor:
MacDonald, Sullivan Francis
It is well-known that every non-negative function in C^{3,1}(R^n) can be written as a finite sum of squares of functions in C^{1,1}(R^n). In this thesis, we generalize this decomposition result to show that if f is a non-negative function in C^{k,a}(
Externí odkaz:
http://hdl.handle.net/11375/28362
In this work we study global boundedness and exponential integrability of weak solutions to degenerate $p$-Poisson equations using an iterative method of De Giorgi type. Given a symmetric, non-negative definite matrix valued function $Q$ defined on a
Externí odkaz:
http://arxiv.org/abs/2210.12441
This paper studies boundedness of weak solutions to $p$-Poisson type equations on a bounded domain $\Omega\subset\mathbb{R}^n$. Given a symmetric, non-negative definite matrix-valued function $Q$ defined on $\Omega$, a weight $v\in L^1_\mathrm{loc}(\
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a78730d89bc45f8a1591f8063a54dbe1
http://arxiv.org/abs/2210.12441
http://arxiv.org/abs/2210.12441