Wavenumber-Explicit Regularity Estimates on the Acoustic Single- and Double-Layer Operators
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DOI: 10.1007/s00020-019-2502-x
Abstract: We prove new, sharp, wavenumber-explicit bounds on the norms of the Helmholtz single- and double-layer boundary-integral operators as mappings from $${L^2({\partial {\Omega }})}\rightarrow H^1({\partial {\Omega }})$$L2(∂Ω)→H1(∂Ω) (where $${\partial {\Omega }}$$∂Ω is the boundary of the… read more here.
Keywords: double layer; single double; partial omega; wavenumber explicit ... See more keywords
Existence and Multiplicity Results for Steklov Problems with p(.)-Growth Conditions
Sign Up to like & getrecommendations! Published in 2018 at "Bulletin of the Iranian Mathematical Society"
DOI: 10.1007/s41980-018-0054-5
Abstract: Using variational methods, we prove in different situations the existence and multiplicity of solutions for the following Steklov problem: $$\begin{aligned} -\text{ div }(a(x, \nabla u))+|u|^{p(x)-2}u= & {} 0, \quad \text {in }\Omega , \\ a(x,… read more here.
Keywords: existence multiplicity; multiplicity results; partial omega; mapsto mathbb ... See more keywords
Modica type estimates and curvature results for overdetermined $ p $-Laplace problems
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DOI: 10.3934/dcds.2025155
Abstract: In this paper we prove Modica type estimates for the following overdetermined $p$-Laplace problem \begin{equation*} \begin{cases} \mathrm{div} \left(|\nabla u|^{p-2}\nabla u\right)+f(u) =0&\mbox{in $\Omega$, } u>0&\mbox{in $\Omega$, } u=0&\mbox{on $\partial\Omega$, } \partial_{\nu} u=-\kappa&\mbox{on $\partial\Omega$, } \end{cases} \end{equation*}… read more here.
Keywords: mbox; type estimates; partial omega; modica type ... See more keywords