Matches in SemOpenAlex for { <https://semopenalex.org/work/W4300872015> ?p ?o ?g. }
Showing items 1 to 66 of
66
with 100 items per page.
- W4300872015 abstract "Bounded weak solutions of Burgers' equation $partial_tu+partial_x(u^2/2)=0$ that are not entropy solutions need in general not be $BV$. Nevertheless it is known that solutions with finite entropy productions have a $BV$-like structure: a rectifiable jump set of dimension one can be identified, outside which $u$ has vanishing mean oscillation at all points. But it is not known whether all points outside this jump set are Lebesgue points, as they would be for $BV$ solutions. In the present article we show that the set of non-Lebesgue points of $u$ has Hausdorff dimension at most one. In contrast with the aforementioned structure result, we need only one particular entropy production to be a finite Radon measure, namely $mu=partial_t (u^2/2)+partial_x(u^3/3)$. We prove Holder regularity at points where $mu$ has finite $(1+alpha)$-dimensional upper density for some $alpha>0$. The proof is inspired by a result of De Lellis, Westdickenberg and the second author : if $mu_+$ has vanishing 1-dimensional upper density, then $u$ is an entropy solution. We obtain a quantitative version of this statement: if $mu_+$ is small then $u$ is close in $L^1$ to an entropy solution." @default.
- W4300872015 created "2022-10-04" @default.
- W4300872015 creator A5006693725 @default.
- W4300872015 creator A5073872018 @default.
- W4300872015 date "2017-04-25" @default.
- W4300872015 modified "2023-09-30" @default.
- W4300872015 title "On the regularity of weak solutions to Burgers equation with finite entropy production" @default.
- W4300872015 doi "https://doi.org/10.48550/arxiv.1704.07633" @default.
- W4300872015 hasPublicationYear "2017" @default.
- W4300872015 type Work @default.
- W4300872015 citedByCount "0" @default.
- W4300872015 crossrefType "posted-content" @default.
- W4300872015 hasAuthorship W4300872015A5006693725 @default.
- W4300872015 hasAuthorship W4300872015A5073872018 @default.
- W4300872015 hasBestOaLocation W43008720151 @default.
- W4300872015 hasConcept C106301342 @default.
- W4300872015 hasConcept C118733216 @default.
- W4300872015 hasConcept C121332964 @default.
- W4300872015 hasConcept C121864883 @default.
- W4300872015 hasConcept C12871628 @default.
- W4300872015 hasConcept C129747778 @default.
- W4300872015 hasConcept C134306372 @default.
- W4300872015 hasConcept C14158598 @default.
- W4300872015 hasConcept C194198291 @default.
- W4300872015 hasConcept C202444582 @default.
- W4300872015 hasConcept C207282930 @default.
- W4300872015 hasConcept C2777105136 @default.
- W4300872015 hasConcept C33923547 @default.
- W4300872015 hasConcept C34388435 @default.
- W4300872015 hasConcept C62520636 @default.
- W4300872015 hasConcept C73225184 @default.
- W4300872015 hasConcept C93779851 @default.
- W4300872015 hasConceptScore W4300872015C106301342 @default.
- W4300872015 hasConceptScore W4300872015C118733216 @default.
- W4300872015 hasConceptScore W4300872015C121332964 @default.
- W4300872015 hasConceptScore W4300872015C121864883 @default.
- W4300872015 hasConceptScore W4300872015C12871628 @default.
- W4300872015 hasConceptScore W4300872015C129747778 @default.
- W4300872015 hasConceptScore W4300872015C134306372 @default.
- W4300872015 hasConceptScore W4300872015C14158598 @default.
- W4300872015 hasConceptScore W4300872015C194198291 @default.
- W4300872015 hasConceptScore W4300872015C202444582 @default.
- W4300872015 hasConceptScore W4300872015C207282930 @default.
- W4300872015 hasConceptScore W4300872015C2777105136 @default.
- W4300872015 hasConceptScore W4300872015C33923547 @default.
- W4300872015 hasConceptScore W4300872015C34388435 @default.
- W4300872015 hasConceptScore W4300872015C62520636 @default.
- W4300872015 hasConceptScore W4300872015C73225184 @default.
- W4300872015 hasConceptScore W4300872015C93779851 @default.
- W4300872015 hasLocation W43008720151 @default.
- W4300872015 hasLocation W43008720152 @default.
- W4300872015 hasOpenAccess W4300872015 @default.
- W4300872015 hasPrimaryLocation W43008720151 @default.
- W4300872015 hasRelatedWork W12722594 @default.
- W4300872015 hasRelatedWork W1534776995 @default.
- W4300872015 hasRelatedWork W1967878345 @default.
- W4300872015 hasRelatedWork W2349062527 @default.
- W4300872015 hasRelatedWork W2591661736 @default.
- W4300872015 hasRelatedWork W2610065195 @default.
- W4300872015 hasRelatedWork W2613139642 @default.
- W4300872015 hasRelatedWork W2963083408 @default.
- W4300872015 hasRelatedWork W4224983188 @default.
- W4300872015 hasRelatedWork W4300872015 @default.
- W4300872015 isParatext "false" @default.
- W4300872015 isRetracted "false" @default.
- W4300872015 workType "article" @default.