Sobolev space
Banach space of functions equipped with a norm that is a combination of Lᵖ-norms of the function itself and its weak derivatives up to a given order
| rdfs:label |
"Sobolev space"@en
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skos:alt |
"Sobolevraum"@de
"Sobolew-Raum"@de
"Sobolewscher Einbettungssatz"@de
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| schema:description |
"Banach space of functions equipped with a norm that is a combination of Lᵖ-norms of the function itself and its weak derivatives up to a given order"@en
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schema:date |
"2026-11-03T00:38:04+00:00"^^xsd:dateTime |
| schema:version | 2564129638 |
| wikibase:identifiers | 15 |
| wikibase:sitelinks | 22 |
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|
p:direct- |
<https:/ |
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p:direct- |
<http:/ |
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p:direct- |
<https:/ |
| wdt:P10283 | "C99730327" |
| wdt:P10376 | "physics-and-astronomy/sobolev-space" |
| wdt:P138 | Sergei Sobolev |
| wdt:P1482 |
<https:/ |
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<https:/ |
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| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi data-mjx-texclass="OP" mathvariant="normal">W</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>s</mi><mo>,</mo><mi>p</mi></mrow></mrow></msup><mo stretchy="false">(</mo><mi>M</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mi>f</mi><mo stretchy="false">∈</mo><msup><mi data-mjx-texclass="OP" mathvariant="normal">L</mi><mrow data-mjx-texclass="ORD"><mi>p</mi></mrow></msup><mo stretchy="false">(</mo><mi>M</mi><mo stretchy="false">)</mo><mo stretchy="false">:</mo><munder><mo stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></mrow></munder><msup><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></mrow></msup><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></msub><mo stretchy="false">⋯</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><msub><mi>μ</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></msub><mi>f</mi><mo stretchy="false">∈</mo><msup><mi data-mjx-texclass="OP" mathvariant="normal">L</mi><mrow data-mjx-texclass="ORD"><mi>p</mi></mrow></msup><mo stretchy="false">(</mo><mi>M</mi><mo>;</mo><mrow data-mjx-texclass="ORD"><mi>𝕂</mi></mrow><mo stretchy="false">)</mo><mspace width="2em"></mspace><mi mathvariant="normal">∀</mi><mi>T</mi><mo stretchy="false">∈</mo><msup><mi mathvariant="normal">Γ</mi><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></msup><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">T</mi></mrow><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">⊗</mo><mi>k</mi></mrow></mrow></msup><mo stretchy="false">)</mo><mo>,</mo><mspace width="0.167em"></mspace><mo stretchy="false">‖</mo><mi>T</mi><mo stretchy="false">‖</mo><mo stretchy="false">≤</mo><mn>1</mn><mo>,</mo><mspace width="0.167em"></mspace><mi>k</mi><mo stretchy="false">≤</mo><mi>s</mi><mo data-mjx-texclass="CLOSE">}</mo></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P279 | Banach space |
| Besov space | |
| Triebel–Lizorkin space | |
| wdt:P2812 | "SobolevSpace" |
| wdt:P31 | mathematical concept |
| wdt:P3827 | "sobolev-spaces" |
| wdt:P4215 | "Sobolev space" |
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| wdt:P5555 |
<http:/ |
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| wdt:P61 | Sergei Sobolev |
| wdt:P6104 | WikiProject Mathematics |
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| wdt:P910 | Category:Sobolev spaces |
| wdt:P9322 | "0229725-Sobolevovy-prostory" |
| wdt:P9621 | "spazi-di-sobolev" |
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