A note on the shift theorem for the Laplacian in polygonal domains
Jens Markus Melenk; Claudio Rojik
Applications of Mathematics (2024)
- Volume: 69, Issue: 5, page 653-693
- ISSN: 0862-7940
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top- Babuška, I., Guo, B. Q., 10.1137/0519014, SIAM J. Math. Anal. 19 (1988), 172-203. (1988) Zbl0647.35021MR0924554DOI10.1137/0519014
- Babuška, I., Guo, B. Q., 10.1137/0520054, SIAM J. Math. Anal. 20 (1989), 763-781. (1989) Zbl0706.35028MR1000721DOI10.1137/0520054
- Babuška, I., Kellogg, R. B., Pitkäranta, J., 10.1007/BF01399326, Numer. Math. 33 (1979), 447-471. (1979) Zbl0423.65057MR0553353DOI10.1007/BF01399326
- Babuška, I., Osborn, J., Eigenvalue problems, Finite Element Methods 1 Handbook of Numerical Analysis II. North Holland, Amsterdam (1991), 641-789. (1991) Zbl0875.65087MR1115240
- Bacuta, C., Interpolation Between Subspaces of Hilbert Spaces and Applications to Shift Theorems for Elliptic Boundary Value Problems and Finite Element Methods: Ph. D. Thesis, Texas A&M University, College Station (2000). (2000) MR2701566
- Bacuta, C., Bramble, J. H., Xu, J., 10.1090/S0025-5718-02-01502-8, Math. Comput. 72 (2003), 1577-1595. (2003) Zbl1031.65133MR1986794DOI10.1090/S0025-5718-02-01502-8
- Bacuta, C., Bramble, J. H., Xu, J., 10.1515/156939503766614117, J. Numer. Math. 11 (2003), 75-94. (2003) Zbl1050.65108MR1987589DOI10.1515/156939503766614117
- Bramble, J. H., Scott, R., 10.1090/S0025-5718-1978-0501990-5, Math. Comput. 32 (1978), 947-954. (1978) Zbl0404.41005MR0501990DOI10.1090/S0025-5718-1978-0501990-5
- Costabel, M., Dauge, M., Nicaise, S., 10.1007/978-1-4419-1341-8_4, Around the Research of Vladimir Maz'ya. I. Function Spaces International Mathematical Series (New York) 11. Springer, New York (2010), 105-136. (2010) Zbl1196.46024MR2723815DOI10.1007/978-1-4419-1341-8_4
- Costabel, M., Dauge, M., Nicaise, S., 10.1142/S0218202512500157, Math. Models Methods Appl. Sci. 22 (2012), Article ID 1250015, 63 pages. (2012) Zbl1257.35056MR2928103DOI10.1142/S0218202512500157
- Costabel, M., Stephan, E., 10.4064/-15-1-175-251, Mathematical Models and Methods in Mechanics Banach Center Publications 15. PWN, Warsaw (1985), 175-251. (1985) Zbl0655.65129MR0874845DOI10.4064/-15-1-175-251
- Costabel, M., Stephan, E., Wendland, W. L., On boundary integral equations of the first kind for the bi-Laplacian in a polygonal domain, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 10 (1983), 197-241. (1983) Zbl0563.45007MR0728434
- Dahlke, S., 10.1016/S0893-9659(99)00075-0, Appl. Math. Lett. 12 (1999), 31-36. (1999) Zbl0940.35064MR1751404DOI10.1016/S0893-9659(99)00075-0
- Dahlke, S., DeVore, R. A., 10.1080/03605309708821252, Commun. Partial Differ. Equations 22 (1997), 1-16. (1997) Zbl0883.35018MR1434135DOI10.1080/03605309708821252
- Dauge, M., 10.1007/BFb0086682, Lecture Notes in Mathematics 1341. Springer, Berlin (1988). (1988) Zbl0668.35001MR0961439DOI10.1007/BFb0086682
- DeVore, R. A., Lorentz, G. G., 10.1007/978-3-662-02888-9, Grundlehren der Mathematischen Wissenschaften 303. Springer, New York (1993). (1993) Zbl0797.41016MR1261635DOI10.1007/978-3-662-02888-9
- Ebmeyer, C., 10.1002/1522-2616(200203)236:1<91::AID-MANA91>3.0.CO;2-1, Math. Nachr. 236 (2002), 91-108. (2002) Zbl1147.35309MR1888558DOI10.1002/1522-2616(200203)236:1<91::AID-MANA91>3.0.CO;2-1
- Ebmeyer, C., Frehse, J., 10.1002/mana.1999.3212030104, Math. Nachr. 203 (1999), 47-74. (1999) Zbl0934.35048MR1698636DOI10.1002/mana.1999.3212030104
- Evans, L. C., 10.1090/gsm/019, Graduate Studies in Mathematics 19. AMS, Providence (2010). (2010) Zbl1194.35001MR1625845DOI10.1090/gsm/019
- Gilbarg, D., Trudinger, N. S., 10.1007/978-3-642-61798-0, Grundlehren der Mathematischen Wissenschaften 224. Springer, Berlin (1983). (1983) Zbl0562.35001MR0737190DOI10.1007/978-3-642-61798-0
- Grisvard, P., Singularities in Boundary Value Problems, Recherches en Mathématiques Appliquées 22. Springer, Berlin (1992). (1992) Zbl0766.35001MR1173209
- Grisvard, P., 10.1137/1.9781611972030, Classics in Applied Mathematics 69. SIAM, Philadelphia (2011). (2011) Zbl1231.35002MR3396210DOI10.1137/1.9781611972030
- Jerison, D. S., Kenig, C. E., 10.1090/S0273-0979-1981-14884-9, Bull. Am. Math. Soc., New Ser. 4 (1981), 203-207. (1981) Zbl0471.35026MR0598688DOI10.1090/S0273-0979-1981-14884-9
- Jerison, D. S., Kenig, C. E., Boundary value problems on Lipschitz domains, Studies in Partial Differential Equations MAA Studies in Mathematics 23. Mathematical Association of America, Washington (1982), 1-68. (1982) Zbl0529.31007MR0716504
- Jerison, D., Kenig, C. E., 10.1006/jfan.1995.1067, J. Funct. Anal. 130 (1995), 161-219. (1995) Zbl0832.35034MR1331981DOI10.1006/jfan.1995.1067
- Kondrat'ev, V. A., Boundary value problems for elliptic equations in domains with conical or angular points, Trudy Moskov. Mat. Obšč. 16 (1967), 209-292 Russian. (1967) Zbl0162.16301MR0226187
- Kozlov, V. A., Maz'ya, V. G., Rossmann, J., 10.1090/surv/052, Mathematical Surveys and Monographs 52. AMS, Providence (1997). (1997) Zbl0947.35004MR1469972DOI10.1090/surv/052
- Maz'ya, V. G., Plamenevskij, B. A., 10.1002/mana.19770760103, Math. Nachr. 76 (1977), 29-60 Russian. (1977) Zbl0359.35024MR601608DOI10.1002/mana.19770760103
- Maz'ya, V. G., Plamenevskij, B. A., 10.1090/trans2/123, Transl., Ser. 2, Am. Math. Soc. 123 (1984), 1-56 translation from Math. Nachr. 81 1978 25-82. (1984) Zbl0554.35035MR492821DOI10.1090/trans2/123
- Maz'ya, V. G., Rossmann, J., 10.1090/surv/162, Mathematical Surveys and Monographs 162. AMS, Providence (2010). (2010) Zbl1196.35005MR2641539DOI10.1090/surv/162
- McLean, W., Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, Cambridge (2000). (2000) Zbl0948.35001MR1742312
- Melenk, J. M., On Generalized Finite-Element Methods: Ph. D. Thesis, University of Maryland, College Park (1995). (1995) MR2692949
- Nazarov, S. A., Plamenevsky, B. A., 10.1515/9783110848915, De Gruyter Expositions in Mathematics 13. Walter de Gruyter, Berlin (1994). (1994) Zbl0806.35001MR1283387DOI10.1515/9783110848915
- Nicaise, S., Polygonal Interface Problems, Methoden und Verfahren der Mathematischen Physik 39. Peter Lang, Frankfurt am Main (1993). (1993) Zbl0794.35040MR1236228
- Rojik, C., 10.34726/hss.2019.65840, Technische Universität Wien, Wien (2019). (2019) DOI10.34726/hss.2019.65840
- Savaré, G., 10.1006/jfan.1997.3158, J. Funct. Anal. 152 (1998), 176-201. (1998) Zbl0889.35018MR1600081DOI10.1006/jfan.1997.3158
- Tartar, L., 10.1007/978-3-540-71483-5, Lecture Notes of the Unione Matematica Italiana 3. Springer, Berlin (2007). (2007) Zbl1126.46001MR2328004DOI10.1007/978-3-540-71483-5
- Triebel, H., Interpolation Theory, Function Spaces, Differential Operators, Johann Ambrosius Barth, Heidelberg (1995). (1995) Zbl0830.46028MR1328645
- Triebel, H., 10.5209/rev_REMA.2002.v15.n2.16910, Rev. Mat. Complut. 15 (2002), 475-524. (2002) Zbl1034.46033MR1951822DOI10.5209/rev_REMA.2002.v15.n2.16910