Matches in SemOpenAlex for { <https://semopenalex.org/work/W4386136090> ?p ?o ?g. }
Showing items 1 to 55 of
55
with 100 items per page.
- W4386136090 abstract "Abstract Motivated by applications to gas filtration problems, we study the regularity of weak solutions to the strongly degenerate parabolic PDE <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mrow> <m:mrow> <m:msub> <m:mi>u</m:mi> <m:mi>t</m:mi> </m:msub> <m:mo>-</m:mo> <m:mrow> <m:mi>div</m:mi> <m:mo></m:mo> <m:mrow> <m:mo maxsize=160% minsize=160%>(</m:mo> <m:mrow> <m:msubsup> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mrow> <m:mo fence=true stretchy=false>|</m:mo> <m:mrow> <m:mi>D</m:mi> <m:mo></m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo fence=true stretchy=false>|</m:mo> </m:mrow> <m:mo>-</m:mo> <m:mi>ν</m:mi> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mo>+</m:mo> <m:mrow> <m:mi>p</m:mi> <m:mo>-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msubsup> <m:mo></m:mo> <m:mfrac> <m:mrow> <m:mi>D</m:mi> <m:mo></m:mo> <m:mi>u</m:mi> </m:mrow> <m:mrow> <m:mo fence=true stretchy=false>|</m:mo> <m:mrow> <m:mi>D</m:mi> <m:mo></m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo fence=true stretchy=false>|</m:mo> </m:mrow> </m:mfrac> </m:mrow> <m:mo maxsize=160% minsize=160%>)</m:mo> </m:mrow> </m:mrow> </m:mrow> <m:mo>=</m:mo> <m:mi>f</m:mi> </m:mrow> <m:mo mathvariant=italic separator=true> </m:mo> <m:mrow> <m:mrow> <m:mtext>in </m:mtext> <m:mo></m:mo> <m:msub> <m:mi mathvariant=normal>Ω</m:mi> <m:mi>T</m:mi> </m:msub> </m:mrow> <m:mo>=</m:mo> <m:mrow> <m:mi mathvariant=normal>Ω</m:mi> <m:mo>×</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi>T</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:mrow> <m:mo>,</m:mo> </m:mrow> </m:math> u_{t}-operatorname{div}Bigl{(}(lvert Durvert-nu)_{+}^{p-1}frac{Du}{% lvert Durvert}Bigr{)}=fquadtext{in }Omega_{T}=Omegatimes(0,T), where Ω is a bounded domain in <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> </m:math> {mathbb{R}^{n}} for <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>n</m:mi> <m:mo>≥</m:mo> <m:mn>2</m:mn> </m:mrow> </m:math> {ngeq 2} , <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>p</m:mi> <m:mo>≥</m:mo> <m:mn>2</m:mn> </m:mrow> </m:math> {pgeq 2} , ν is a positive constant and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mrow> <m:mo rspace=4.2pt stretchy=false>(</m:mo> <m:mo rspace=4.2pt>⋅</m:mo> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mo>+</m:mo> </m:msub> </m:math> {(,cdot,)_{+}} stands for the positive part. Assuming that the datum f belongs to a suitable Lebesgue–Sobolev parabolic space, we establish the Sobolev spatial regularity of a nonlinear function of the spatial gradient of the weak solutions, which in turn implies the existence of the weak time derivative <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi>u</m:mi> <m:mi>t</m:mi> </m:msub> </m:math> {u_{t}} . The main novelty here is that the structure function of the above equation satisfies standard growth and ellipticity conditions only outside a ball with radius ν centered at the origin. We would like to point out that the first result obtained here can be considered, on the one hand, as the parabolic counterpart of an elliptic result established in [L. Brasco, G. Carlier and F. Santambrogio, Congested traffic dynamics, weak flows and very degenerate elliptic equations [corrected version of mr2584740], J. Math. Pures Appl. (9) 93 2010, 6, 652–671], and on the other hand as the extension to a strongly degenerate context of some known results for less degenerate parabolic equations." @default.
- W4386136090 created "2023-08-25" @default.
- W4386136090 creator A5059354275 @default.
- W4386136090 creator A5070581878 @default.
- W4386136090 date "2023-08-25" @default.
- W4386136090 modified "2023-09-30" @default.
- W4386136090 title "Regularity results for a class of widely degenerate parabolic equations" @default.
- W4386136090 cites W1504810697 @default.
- W4386136090 cites W1600401428 @default.
- W4386136090 cites W1986632944 @default.
- W4386136090 cites W1996052204 @default.
- W4386136090 cites W2019999510 @default.
- W4386136090 cites W2080684206 @default.
- W4386136090 cites W2093672363 @default.
- W4386136090 cites W2123762546 @default.
- W4386136090 cites W2166231663 @default.
- W4386136090 cites W2393414163 @default.
- W4386136090 cites W2559765453 @default.
- W4386136090 cites W2941765503 @default.
- W4386136090 cites W2964107926 @default.
- W4386136090 cites W3143850007 @default.
- W4386136090 cites W4220996421 @default.
- W4386136090 cites W4235853207 @default.
- W4386136090 cites W4367556807 @default.
- W4386136090 cites W644710670 @default.
- W4386136090 doi "https://doi.org/10.1515/acv-2022-0062" @default.
- W4386136090 hasPublicationYear "2023" @default.
- W4386136090 type Work @default.
- W4386136090 citedByCount "1" @default.
- W4386136090 countsByYear W43861360902023 @default.
- W4386136090 crossrefType "journal-article" @default.
- W4386136090 hasAuthorship W4386136090A5059354275 @default.
- W4386136090 hasAuthorship W4386136090A5070581878 @default.
- W4386136090 hasConcept C121332964 @default.
- W4386136090 hasConceptScore W4386136090C121332964 @default.
- W4386136090 hasFunder F4320309590 @default.
- W4386136090 hasFunder F4320333369 @default.
- W4386136090 hasIssue "0" @default.
- W4386136090 hasLocation W43861360901 @default.
- W4386136090 hasOpenAccess W4386136090 @default.
- W4386136090 hasPrimaryLocation W43861360901 @default.
- W4386136090 hasRelatedWork W2271181815 @default.
- W4386136090 hasRelatedWork W2902782467 @default.
- W4386136090 hasRelatedWork W2935759653 @default.
- W4386136090 hasRelatedWork W3105167352 @default.
- W4386136090 hasRelatedWork W3148032049 @default.
- W4386136090 hasRelatedWork W54078636 @default.
- W4386136090 hasRelatedWork W1501425562 @default.
- W4386136090 hasRelatedWork W2298861036 @default.
- W4386136090 hasRelatedWork W2954470139 @default.
- W4386136090 hasRelatedWork W3084825885 @default.
- W4386136090 hasVolume "0" @default.
- W4386136090 isParatext "false" @default.
- W4386136090 isRetracted "false" @default.
- W4386136090 workType "article" @default.