Symmetry and stability of non-negative solutions to degenerate elliptic equations in a ball Article Swipe
Friedemann Brock
,
Peter Takáč
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1090/proc/15838
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1090/proc/15838
We consider non-negative distributional solutions to the equation in a ball , with on , where is continuous and non-increasing in the first variable and , with and for . According to a result of the first author, the solutions satisfy a certain ‘local’ type of symmetry. Using this, we first prove that the solutions are radially symmetric provided that satisfies appropriate growth conditions near its zeros. In a second part we study the autonomous case, . The solutions of the equation are critical points for an associated variation problem. We show under rather mild conditions that global and local minimizers of the variational problem are radial.
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- article
- Language
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- Landing Page
- https://doi.org/10.1090/proc/15838
- https://www.ams.org/proc/2022-150-04/S0002-9939-2022-15838-9/S0002-9939-2022-15838-9.pdf
- OA Status
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- 1
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https://openalex.org/W2996275382Canonical identifier for this work in OpenAlex
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https://doi.org/10.1090/proc/15838Digital Object Identifier
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Symmetry and stability of non-negative solutions to degenerate elliptic equations in a ballWork title
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articleOpenAlex work type
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lvPrimary language
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2021Year of publication
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2021-09-29Full publication date if available
- Authors
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Friedemann Brock, Peter TakáčList of authors in order
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https://doi.org/10.1090/proc/15838Publisher landing page
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https://www.ams.org/proc/2022-150-04/S0002-9939-2022-15838-9/S0002-9939-2022-15838-9.pdfDirect link to full text PDF
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YesWhether a free full text is available
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bronzeOpen access status per OpenAlex
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https://www.ams.org/proc/2022-150-04/S0002-9939-2022-15838-9/S0002-9939-2022-15838-9.pdfDirect OA link when available
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Degenerate energy levels, Ball (mathematics), Symmetry (geometry), Mathematics, Mathematical analysis, Mathematical physics, Classical mechanics, Physics, Geometry, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.alttext="u | 9, 206 |
| abstract_inverted_index.associated | 507 |
| abstract_inverted_index.autonomous | 469 |
| abstract_inverted_index.conditions | 458, 515 |
| abstract_inverted_index.continuous | 260 |
| abstract_inverted_index.element-of | 10, 273 |
| abstract_inverted_index.minimizers | 520 |
| abstract_inverted_index.u|)|\nabla | 169 |
| abstract_inverted_index.</mml:math> | 54, 177, 199, 218, 244, 257, 334, 361, 392, 411, 453, 495 |
| abstract_inverted_index.</mml:mrow> | 45, 109, 117, 124, 133, 138, 153, 159, 164, 214, 239, 324, 357, 388, 407, 491 |
| abstract_inverted_index.</mml:msub> | 39, 195, 238 |
| abstract_inverted_index.</mml:msup> | 32, 139, 303, 380 |
| abstract_inverted_index.<mml:mover> | 35 |
| abstract_inverted_index.Superscript | 13, 79, 276 |
| abstract_inverted_index.appropriate | 456 |
| abstract_inverted_index.variational | 523 |
| abstract_inverted_index.‘local’ | 426 |
| abstract_inverted_index.</mml:mover> | 42 |
| abstract_inverted_index.alttext="f"> | 251, 447 |
| abstract_inverted_index.greater-than | 373, 400 |
| abstract_inverted_index.intersection | 286 |
| abstract_inverted_index.left-bracket | 67, 289 |
| abstract_inverted_index.non-negative | 2 |
| abstract_inverted_index.right-bracket | 85 |
| abstract_inverted_index.alttext="minus | 63 |
| abstract_inverted_index.alttext="upper | 186 |
| abstract_inverted_index.distributional | 3 |
| abstract_inverted_index.non-increasing | 262 |
| abstract_inverted_index.<inline-formula | 5, 59, 182, 202, 221, 247, 268, 337, 364, 395, 443, 471 |
| abstract_inverted_index.<mml:annotation | 46, 165, 196, 215, 240, 254, 325, 358, 389, 408, 450, 492 |
| abstract_inverted_index.<mml:semantics> | 25, 95, 191, 209, 231, 252, 296, 347, 375, 402, 448, 481 |
| abstract_inverted_index.</mml:semantics> | 53, 176, 198, 217, 243, 256, 333, 360, 391, 410, 452, 494 |
| abstract_inverted_index.EndAbsoluteValue | 73, 78, 91 |
| abstract_inverted_index.left-parenthesis | 16, 69, 88, 279, 342, 370, 478 |
| abstract_inverted_index.</inline-formula> | 55, 178, 219, 258, 362, 393, 454 |
| abstract_inverted_index.right-parenthesis | 74, 285, 344, 372 |
| abstract_inverted_index.)</mml:annotation> | 52, 332 |
| abstract_inverted_index.</inline-formula>, | 200, 245, 335 |
| abstract_inverted_index.</inline-formula>. | 412, 496 |
| abstract_inverted_index.<mml:mi>B</mml:mi> | 37, 193, 236 |
| abstract_inverted_index.<mml:mi>C</mml:mi> | 30, 301, 314 |
| abstract_inverted_index.<mml:mi>R</mml:mi> | 38, 194, 237 |
| abstract_inverted_index.<mml:mi>f</mml:mi> | 146, 253, 449, 483, 485 |
| abstract_inverted_index.<mml:mi>g</mml:mi> | 102, 298, 349, 378 |
| abstract_inverted_index.<mml:mi>t</mml:mi> | 383, 404 |
| abstract_inverted_index.<mml:mi>u</mml:mi> | 27, 112, 127, 142, 161, 211, 488 |
| abstract_inverted_index.<mml:mi>x</mml:mi> | 154 |
| abstract_inverted_index.<mml:mn>0</mml:mn> | 213, 306, 317, 352, 356, 387, 406 |
| abstract_inverted_index.<mml:mn>1</mml:mn> | 31, 137, 302 |
| abstract_inverted_index.<mml:mo>+</mml:mo> | 308, 319 |
| abstract_inverted_index.<mml:mo>,</mml:mo> | 160, 307, 318 |
| abstract_inverted_index.<mml:mo>=</mml:mo> | 145, 212, 355, 484 |
| abstract_inverted_index.StartAbsoluteValue | 70, 75, 89 |
| abstract_inverted_index.right-parenthesis"> | 24, 94, 295, 480 |
| abstract_inverted_index.<mml:mi>div</mml:mi> | 98 |
| abstract_inverted_index.<mml:mo>′</mml:mo> | 379 |
| abstract_inverted_index.<mml:mo></mml:mo> | 99 |
| abstract_inverted_index.<mml:mo>∈</mml:mo> | 28, 299 |
| abstract_inverted_index.<mml:mo>−</mml:mo> | 97, 136 |
| abstract_inverted_index.<mml:mo>∩</mml:mo> | 313 |
| abstract_inverted_index.B_R</mml:annotation> | 242 |
| abstract_inverted_index.<mml:mo>></mml:mo> | 386, 405 |
| abstract_inverted_index.class="MJX-TeXAtom-ORD"> | 106, 114, 121, 130, 135, 150, 156 |
| abstract_inverted_index.f(|x|,u)</mml:annotation> | 175 |
| abstract_inverted_index.accent="false">¯</mml:mo> | 41 |
| abstract_inverted_index.content-type="math/mathml"> | 6, 60, 183, 203, 222, 248, 269, 338, 365, 396, 444, 472 |
| abstract_inverted_index.stretchy="false">(</mml:mo> | 34, 104, 148, 305, 351, 382, 487 |
| abstract_inverted_index.stretchy="false">)</mml:mo> | 44, 119, 163, 312, 323, 354, 385, 490 |
| abstract_inverted_index.stretchy="false">[</mml:mo> | 101, 316 |
| abstract_inverted_index.stretchy="false">]</mml:mo> | 144 |
| abstract_inverted_index.stretchy="false">|</mml:mo> | 108, 116, 123, 132, 152, 158 |
| abstract_inverted_index.alttext="partial-differential | 225 |
| abstract_inverted_index.encoding="application/x-tex">g\in | 326 |
| abstract_inverted_index.encoding="application/x-tex">u\in | 47 |
| abstract_inverted_index.mathvariant="normal">∂</mml:mi> | 234 |
| abstract_inverted_index.mathvariant="normal">∇</mml:mi> | 111, 126, 141 |
| abstract_inverted_index.mathvariant="normal">∞</mml:mi> | 310, 321 |
| abstract_inverted_index.encoding="application/x-tex">\partial | 241 |
| abstract_inverted_index.encoding="application/x-tex">-\operatorname | 166 |
| abstract_inverted_index.xmlns:mml="http://www.w3.org/1998/Math/MathML" | 8, 62, 185, 205, 224, 250, 271, 340, 367, 398, 446, 474 |
| abstract_inverted_index.encoding="application/x-tex">f</mml:annotation> | 255, 451 |
| abstract_inverted_index.encoding="application/x-tex">B_R</mml:annotation> | 197 |
| abstract_inverted_index.encoding="application/x-tex">u=0</mml:annotation> | 216 |
| abstract_inverted_index.encoding="application/x-tex">f=f(u)</mml:annotation> | 493 |
| abstract_inverted_index.encoding="application/x-tex">g(0)=0</mml:annotation> | 359 |
| abstract_inverted_index.encoding="application/x-tex">t>0</mml:annotation> | 409 |
| abstract_inverted_index.encoding="application/x-tex">g’(t)>0</mml:annotation> | 390 |
| cited_by_percentile_year.max | 93 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.4706588 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |