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• W2912121431 abstract "Abstract This paper studies a singular perturbation result for a class of generalized diffusive logistic equations, <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mi>d</m:mi> <m:mo>⁢</m:mo> <m:mi mathvariant=script>ℒ</m:mi> <m:mo>⁢</m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo>=</m:mo> <m:mrow> <m:mi>u</m:mi> <m:mo>⁢</m:mo> <m:mi>h</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>u</m:mi> <m:mo>,</m:mo> <m:mi>x</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> {dmathcal{L}u=uh(u,x)} , under non-classical mixed boundary conditions, <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mi mathvariant=script>ℬ</m:mi> <m:mo>⁢</m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> {mathcal{B}u=0} on <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mo>∂</m:mo> <m:mo>⁡</m:mo> <m:mi mathvariant=normal>Ω</m:mi> </m:mrow> </m:math> {partialOmega} . Most of the precursors of this result dealt with Dirichlet boundary conditions and self-adjoint second order elliptic operators. To overcome the new technical difficulties originated by the generality of the new setting, we have characterized the regularity of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mo>∂</m:mo> <m:mo>⁡</m:mo> <m:mi mathvariant=normal>Ω</m:mi> </m:mrow> </m:math> {partialOmega} through the regularity of the associated conormal projections and conormal distances . This seems to be a new result of a huge relevance on its own. It actually complements some classical findings of Serrin, [39], Gilbarg and Trudinger, [21], Krantz and Parks, [27], Foote, [18] and Li and Nirenberg [28] concerning the regularity of the inner distance function to the boundary." @default.
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• W2912121431 date "2018-10-31" @default.
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• W2912121431 title "The Singular Perturbation Problem for a Class of Generalized Logistic Equations Under Non-classical Mixed Boundary Conditions" @default.
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• W2912121431 doi "https://doi.org/10.1515/ans-2018-2034" @default.
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