Nonexistence of solutions for quasilinear elliptic equations with p-growth in the gradient
We study the nonexistence of weak solutions in $W^{1,p}_{{ m loc}}(Omega)$ for a class of quasilinear elliptic boundary-value problems with natural growth in the gradient. Nonsolvability conditions involve general domains with possible singularities of the right-hand side. In particular, we show tha...
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| Format: | Article |
| Language: | English |
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Texas State University
2002-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2002/54/abstr.html |
| _version_ | 1819200417914945536 |
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| author | Darko Zubrinic |
| author_facet | Darko Zubrinic |
| author_sort | Darko Zubrinic |
| collection | DOAJ |
| description | We study the nonexistence of weak solutions in $W^{1,p}_{{ m loc}}(Omega)$ for a class of quasilinear elliptic boundary-value problems with natural growth in the gradient. Nonsolvability conditions involve general domains with possible singularities of the right-hand side. In particular, we show that if the data on the right-hand side are sufficiently large, or if inner radius of $Omega$ is large, then there are no weak solutions. |
| first_indexed | 2024-12-23T03:31:54Z |
| format | Article |
| id | doaj.art-bf91f2d3c9024ff2848cce782355510e |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-23T03:31:54Z |
| publishDate | 2002-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-bf91f2d3c9024ff2848cce782355510e2022-12-21T18:01:40ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912002-06-0120025418Nonexistence of solutions for quasilinear elliptic equations with p-growth in the gradientDarko ZubrinicWe study the nonexistence of weak solutions in $W^{1,p}_{{ m loc}}(Omega)$ for a class of quasilinear elliptic boundary-value problems with natural growth in the gradient. Nonsolvability conditions involve general domains with possible singularities of the right-hand side. In particular, we show that if the data on the right-hand side are sufficiently large, or if inner radius of $Omega$ is large, then there are no weak solutions.http://ejde.math.txstate.edu/Volumes/2002/54/abstr.htmlQuasilinear ellipticexistencenonexistencegeometry of domains. |
| spellingShingle | Darko Zubrinic Nonexistence of solutions for quasilinear elliptic equations with p-growth in the gradient Electronic Journal of Differential Equations Quasilinear elliptic existence nonexistence geometry of domains. |
| title | Nonexistence of solutions for quasilinear elliptic equations with p-growth in the gradient |
| title_full | Nonexistence of solutions for quasilinear elliptic equations with p-growth in the gradient |
| title_fullStr | Nonexistence of solutions for quasilinear elliptic equations with p-growth in the gradient |
| title_full_unstemmed | Nonexistence of solutions for quasilinear elliptic equations with p-growth in the gradient |
| title_short | Nonexistence of solutions for quasilinear elliptic equations with p-growth in the gradient |
| title_sort | nonexistence of solutions for quasilinear elliptic equations with p growth in the gradient |
| topic | Quasilinear elliptic existence nonexistence geometry of domains. |
| url | http://ejde.math.txstate.edu/Volumes/2002/54/abstr.html |
| work_keys_str_mv | AT darkozubrinic nonexistenceofsolutionsforquasilinearellipticequationswithpgrowthinthegradient |