Nonlinear partial differential equations and free boundaries: 1 Elliptic equations
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Pitman
1985
|
| Edition: | 1. publ. |
| Series: | Research notes in mathematics
106 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 323 S. graph. Darst. |
| ISBN: | 0273085727 |
Staff View
MARC
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| 245 | 1 | 0 | |a Nonlinear partial differential equations and free boundaries |n 1 |p Elliptic equations |c J. I. Díaz |
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| 264 | 1 | |a Boston [u.a.] |b Pitman |c 1985 | |
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Record in the Search Index
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| adam_text | Contents
PREFACE
INTRODUCTION 1
NOTATION 14
CHAPTER 1. THE FREE BOUNDARY IN THE DIRICHLET PROBLEM FOR SECOND
ORDER ELLIPTIC QUASILINEAR EQUATIONS 16
1.1. On the existence of the free boundary 17
l.la.Onedimensional and radially symmetric solutions 22
1.1b.Interior estimates. Local super and subsolutions 33
1.1c.Boundary estimates. Nondiffusion of the support 42
1.Id.Solutions with compact support.Global super and
subsolutions 48
1.2. Nonexistence of the free boundary. Positivity of solutions 54
1.2a. On the balance diffusion absorption. A strong maxi¬
mum principle 54
1.2b. Criteria on the balance between the data and the
domain. Gradient estimates 57
1.3. Some applications of the symmetric rearrangement of a func¬
tion 63
1.3a. A general result. An isoperimetric inequality for the
null set 67
1.3b. On the symmetry of the solution and of its null set 83
1.3c. The free boundary for equations with a general non¬
linear diffusion term 86
1.4. Further results on the free boundary for semilinear equa¬
tions 90
1.4a. On the behaviour of solutions near the free boundary 90
1.4b. Lebesgue and Hausdorff measure of the free boundary.
Application to domains of boundary having nonnegative
mean curvature 96
1.4c. Regularity of the free boundary and dependence with
respect to a parameter in the equation 104
1.4d. Geometrical properties of the free boundary 108
1.5. Bibliographical notes 113
CHAPTER 2. THE FREE BOUNDARY IN OTHER SECOND ORDER NON LINEAR
PROBLEMS 118
2.1. Equations with nonmonotone perturbation term 119
2.1a. A nonmonotone semilinear equation in exothermical
chemical reactions 120
2.1b. A nonlinear system 124
2.1c. Equilibrium solutions of a degenerate parabolic
equation in biological population models 125
2.Id. Nonnegative radial solutions of a nonmonotone
semilinear equation in V. 131
2.2. Variational Inequalities and multivalued equations 137
2.2a. Existence and location of the free boundary
Solutions with compact support 141
2.2b. Rearrangement and multivalued equations 151
2.2c. Further results 157
2.3. A singular equation 161
2.3a. On the variational and other limiting solutions 161
2.3b. On the existence of the free boundary 168
2.4. Nonisotropic equations 177
2.4a. Equations in divergenece form. On the diffusion
convection balance 179
2.4b. Fully nonlinear equations. Optimal strategy for
the Hamilton Jacobi Bellman equation 184
2.5. Other boundary value problems 196
2.5a. Nonlinear equations with other boundary conditions 197
2.5b. The Signorini problem 201
2.6. Bibliographical notes 207
CHAPTER 3. EXISTENCE AND LOCATION OF THE FREE BOUNDARY BY MEANS
OF ENERGY METHODS 212
3.1. Second order quasilinear equations 212
3.1a. The main result 212
3.1b. Proof of the interpolation trace Lemma 223
3.2. Quasilinear elliptic equations of arbitrary order 226
3.3. Bibliographical notes 235
CHAPTER 4. THE GENERAL THEORY FOR SECOND ORDER NONLINEAR ELLIPTIC
EQUATIONS: A PARTICULAR OVERVIEW 237
4.1. Solutions in the energy space 238
4.1a. Some first existence results via minimization of
functionals 238
4.1b. Some extensions of variational problems: Monotone
operators and their generalizations 248
4.1c. On the regularity of solutions. L? estimates 257
4.1d. Uniqueness and comparison results. Existence via
comparison 263
4.2. Solutions outside the energy space 273
4.2a. Semilinear equations in L (fi) and other spaces 275
4.2b. Abstract results. Accretive operators. Application
to quasilinear equations 284
4.3. Bibliographical notes 290
REFERENCES 292
INDEX 320
|
| any_adam_object | 1 |
| author | Díaz, Jesús Ildefonso 1950- |
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| author_variant | j i d ji jid |
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| bvnumber | BV000513827 |
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| discipline | Mathematik |
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| id | DE-604.BV000513827 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:15:05Z |
| institution | BVB |
| isbn | 0273085727 |
| language | English |
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| owner_facet | DE-12 DE-355 DE-BY-UBR DE-824 DE-11 DE-188 |
| physical | 323 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Pitman |
| record_format | marc |
| series | Research notes in mathematics |
| series2 | Research notes in mathematics |
| spelling | Díaz, Jesús Ildefonso 1950- Verfasser (DE-588)123470293 aut Nonlinear partial differential equations and free boundaries 1 Elliptic equations J. I. Díaz 1. publ. Boston [u.a.] Pitman 1985 323 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Research notes in mathematics 106 Research notes in mathematics ... Freies Randwertproblem (DE-588)4155303-2 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Randwertproblem (DE-588)4048395-2 s DE-604 Freies Randwertproblem (DE-588)4155303-2 s (DE-604)BV000513826 1 Research notes in mathematics 106 (DE-604)BV000000039 106 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000317279&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Díaz, Jesús Ildefonso 1950- Nonlinear partial differential equations and free boundaries Research notes in mathematics Freies Randwertproblem (DE-588)4155303-2 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4155303-2 (DE-588)4128900-6 (DE-588)4048395-2 |
| title | Nonlinear partial differential equations and free boundaries |
| title_auth | Nonlinear partial differential equations and free boundaries |
| title_exact_search | Nonlinear partial differential equations and free boundaries |
| title_full | Nonlinear partial differential equations and free boundaries 1 Elliptic equations J. I. Díaz |
| title_fullStr | Nonlinear partial differential equations and free boundaries 1 Elliptic equations J. I. Díaz |
| title_full_unstemmed | Nonlinear partial differential equations and free boundaries 1 Elliptic equations J. I. Díaz |
| title_short | Nonlinear partial differential equations and free boundaries |
| title_sort | nonlinear partial differential equations and free boundaries elliptic equations |
| topic | Freies Randwertproblem (DE-588)4155303-2 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Freies Randwertproblem Nichtlineare partielle Differentialgleichung Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000317279&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000513826 (DE-604)BV000000039 |
| work_keys_str_mv | AT diazjesusildefonso nonlinearpartialdifferentialequationsandfreeboundaries1 |